scientific article; zbMATH DE number 802623
From MaRDI portal
Publication:4849745
zbMath0837.58001MaRDI QIDQ4849745
Publication date: 4 October 1995
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
symmetryequivalenceinvariantsdifferential formsdifferential equationsvariational problemsvector fields
Linear ordinary differential equations and systems (34A30) Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)
Related Items
Lie algebroids and Cartan’s method of equivalence ⋮ Symmetry of stochastic non-variational differential equations ⋮ Position dependent non-linear Schrödinger hierarchies: involutivity, commutation relations, renormalisation and classical invariants ⋮ Integrable motions of curves in \(S^{1} \times \mathbb R\) ⋮ Geometric interpretation of fractional-order derivative ⋮ A geometric approach to nonlinear dissipative balanced reduction. I: Exogenous signals ⋮ Two-dimensional defective crystals with non-constant dislocation density and unimodular solvable group structure ⋮ Symmetries of trivial systems of ODEs of mixed order ⋮ The problem of invariance for covariant Hamiltonians ⋮ Variational integrators for nonvariational partial differential equations ⋮ I. GM-sets applied to Lie theory ⋮ Involutive moving frames. II: The Lie-Tresse theorem ⋮ A new incremental algorithm for computing Groebner bases ⋮ Degree bounds for Gröbner bases of low-dimensional polynomial ideals ⋮ A new algorithm for computing comprehensive Gröbner systems ⋮ Finding all bessel type solutions for linear differential equations with rational function coefficients ⋮ Simultaneously row- and column-reduced higher-order linear differential systems ⋮ Consistency of finite difference approximations for linear PDE systems and its algorithmic verification ⋮ Computation with semialgebraic sets represented by cylindrical algebraic formulas ⋮ Black-box/white-box simplification and applications to quantifier elimination ⋮ Parametric quantified SAT solving ⋮ A method for semi-rectifying algebraic and differential systems using scaling type lie point symmetries with linear algebra ⋮ Absolute factoring of non-holonomic ideals in the plane ⋮ Algorithms for Bernstein--Sato polynomials and multiplier ideals ⋮ Global optimization of polynomials using generalized critical values and sums of squares ⋮ A Slice algorithm for corners and Hilbert-Poincaré series of monomial ideals ⋮ Composition collisions and projective polynomials ⋮ Decomposition of generic multivariate polynomials ⋮ Chebyshev interpolation polynomial-based tools for rigorous computing ⋮ Blind image deconvolution via fast approximate GCD ⋮ Polynomial integration on regions defined by a triangle and a conic ⋮ Computing the singularities of rational space curves ⋮ Solving schubert problems with Littlewood-Richardson homotopies ⋮ When can we detect that a P-finite sequence is positive? ⋮ Complexity of creative telescoping for bivariate rational functions ⋮ Partial denominator bounds for partial linear difference equations ⋮ Real and complex polynomial root-finding with eigen-solving and preprocessing ⋮ Computing the radius of positive semidefiniteness of a multivariate real polynomial via a dual of Seidenberg's method ⋮ Random polynomials and expected complexity of bisection methods for real solving ⋮ The DMM bound ⋮ Solving Bezout-like polynomial equations for the design of interpolatory subdivision schemes ⋮ Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology ⋮ Output-sensitive decoding for redundant residue systems ⋮ A Strassen-like matrix multiplication suited for squaring and higher power computation ⋮ Computing specified generators of structured matrix inverses ⋮ Yet another block Lanczos algorithm ⋮ Liouvillian solutions of irreducible second order linear difference equations ⋮ Solving recurrence relations using local invariants ⋮ On some decidable and undecidable problems related to q-difference equations with parameters ⋮ Iterative Toom-Cook methods for very unbalanced long integer multiplication ⋮ An in-place truncated fourier transform and applications to polynomial multiplication ⋮ Randomized NP-completeness for p -adic rational roots of sparse polynomials in one variable ⋮ Signatures of algebraic curves via numerical algebraic geometry ⋮ On geometry of 2-nondegenerate CR structures of hypersurface type and flag structures on leaf spaces of Levi foliations ⋮ Lax representations with non-removable parameters and integrable hierarchies of PDEs via exotic cohomology of symmetry algebras ⋮ Massless scalars and higher-spin BMS in any dimension ⋮ Integrable systems and invariant curve flows in centro-equiaffine symplectic geometry ⋮ Tangent bundle viewpoint of the Lorenz system and its chaotic behavior ⋮ Lagrangian multiforms on Lie groups and non-commuting flows ⋮ A recursion operator for the universal hierarchy equation via Cartan's method of equivalence ⋮ Symmetries of second-order systems of ODEs and integrability ⋮ Generalized transvectants and Siegel modular forms ⋮ Coverings of differential equations and Cartan's structure theory of Lie pseudo-groups ⋮ Conservation laws and potential symmetries of linear parabolic equations ⋮ Diffeomorphism-invariant covariant Hamiltonians of a linear frame and a linear connection ⋮ Transformation groups on real plane and their differential invariants ⋮ Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements ⋮ Local equivalence problem for a second order complete scalar system of partial differencial equations with \(n\) independent variables ⋮ Maximum rank of a Legendrian web ⋮ Lie symmetries and differential Galois groups of linear equations ⋮ Lagrangian curves in a 4-dimensional affine symplectic space ⋮ Three-component WKI equation and curve motion flow in Euclidean and Minkowski space ⋮ Lie symmetries and CR geometry ⋮ Differential invariants of a class of Lagrangian systems with two degrees of freedom ⋮ Second order ODEs under area-preserving maps ⋮ II. GM-manifolds and unique structure ⋮ On relation between algebraic and ordinary differential algebraic invariants of motion groups ⋮ On the period function for a family of complex differential equations ⋮ Lie remarkable partial differential equations characterized by Lie algebras of point symmetries ⋮ Pattern generation, topology, and non-holonomic systems ⋮ Exact solutions via equivalence transformations of variable-coefficient fifth-order KdV equations ⋮ Suppression of Sommerfeld effect in a non-ideal discrete rotor system with fractional order external damping ⋮ Characterization of the Newtonian free particle system in \(m\geqslant 2\) dependent variables ⋮ On the algorithmic linearizability of nonlinear ordinary differential equations ⋮ Differential invariants for third-order evolution equations ⋮ The group classification of Lane-Emden systems ⋮ Group classification of nonlinear evolution equations: semi-simple groups of contact transformations ⋮ Involutive moving frames ⋮ On the geometry of twisted symmetries: gauging and coverings ⋮ Biholomorphic equivalence to totally nondegenerate model CR manifolds ⋮ On the variational problems without having desired variational symmetries ⋮ On the local classification of smooth maps induced by Newton's method ⋮ NumGfun ⋮ Lie symmetries of quasihomogeneous polynomial planar vector fields and certain perturbations ⋮ Linearization of control systems: a Lie series approach ⋮ Homogeneous geodesics of non-reductive homogeneous pseudo-Riemannian 4-manifolds ⋮ Third-order ODEs and four-dimensional split signature Einstein metrics ⋮ An invitation to modern group analysis of differential equations ⋮ Nontrivial 1-parameter families of zero-curvature representations obtained via symmetry actions ⋮ The hole argument and some physical and philosophical implications ⋮ Flat \((2,3,5)\)-distributions and Chazy's equations ⋮ Symmetry properties of a nonlinear acoustics model ⋮ A simple direct method to find equivalence transformations of a generalized nonlinear Schrödinger equation and a generalized KdV equation ⋮ The structure of uniform discrete defective crystals ⋮ Geodesic matching with free extremities ⋮ On the geometry of \(y^{(4)}=f(x,y,y^{\prime },y^{\prime\prime },y^{\prime\prime\prime })\) ⋮ Strictly nearly Kähler 6-manifolds are not compatible with symplectic forms ⋮ 3-dimensional left-invariant sub-Lorentzian contact structures ⋮ Cartan equivalence problem for 5-dimensional bracket-generating CR manifolds in \(\mathbb C^4\) ⋮ Affine differential invariants of functions on the plane ⋮ Inductive moving frames ⋮ On post-Lie algebras, Lie-Butcher series and moving frames ⋮ Fuzzy differential invariant (FDI) ⋮ Symmetry analysis, integrability and completeness of geodesics of a double of the affine Lie group of the real line ⋮ Variational problems with symmetries: a Pfaffian system approach ⋮ Extensions of invariant signatures for object recognition ⋮ Differential invariants of the one-dimensional quasi-linear second-order evolution equation ⋮ On differential equations characterized by their Lie point symmetries ⋮ Generating differential invariants ⋮ Conditional symmetries and the canonical quantization of constrained minisuperspace actions: the Schwarzschild case ⋮ Symplectic invariants for curves and integrable systems in similarity symplectic geometry ⋮ Symmetries of sub-Riemannian surfaces ⋮ Reduction of balance laws in \((3+1)\)-dimensions to autonomous conservation laws by means of equivalence transformations ⋮ Construction of autonomous conservation laws ⋮ Reductions for Kundu-Eckhaus equation via Lie symmetry analysis ⋮ Steady-state dynamics of a non-ideal rotor with internal damping and gyroscopic effects ⋮ Integrable equations and recursion operators in planar Klein geometries ⋮ Invariants of objects and their images under surjective maps ⋮ Differential invariants and symmetry: Riemannian metrics and beyond ⋮ Integrable dispersionless PDEs in 4D, their symmetry pseudogroups and deformations ⋮ Equivalence for differential equations ⋮ Unsteady solutions of Euler equations generated by steady solutions ⋮ Moving frames, geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors ⋮ Moduli spaces of model real submanifolds: two alternative approaches ⋮ Symmetry analysis and conservation laws of the geodesic equations for the Reissner-Nordström de Sitter black hole with a global monopole ⋮ Holomorphic Cartan geometries on uniruled surfaces ⋮ On the cohomology of the invariant Euler--Lagrange complex ⋮ On the invariants of two dimensional linear parabolic equations ⋮ An invariant observer for a chemostat model ⋮ On-shell extension of distributions ⋮ Application of canonical coordinates for solving single-freedom constraint mechanical systems ⋮ A classification of locally homogeneous affine connections on compact surfaces ⋮ Projective-type differential invariants and geometric curve evolutions of KdV-type in flat homogeneous manifolds ⋮ On computing joint invariants of vector fields ⋮ Gauge symmetries in 2D field theory ⋮ Differential invariants for quasi-linear and semi-linear wave-type equations ⋮ Cartan's structure theory of symmetry pseudo-groups, coverings and multi-valued solutions for the Khokhlov-Zabolotskaya equation ⋮ On local integrability conditions of jet groupoids ⋮ Singular invariant structures for Lie algebras admitted by a system of second-order ODEs ⋮ Symmetries and first integrals of differential equations ⋮ Unreasonable effectiveness of symmetry in physics ⋮ Nonlinear first order PDEs reducible to autonomous form polynomially homogeneous in the derivatives ⋮ Conformal differential invariants ⋮ Deformed cohomologies of symmetry pseudo-groups and coverings of differential equations ⋮ Routh reduction and Cartan mechanics ⋮ Invariants of two- and three-dimensional hyperbolic equations ⋮ \(\lambda\)-symmetries, isochronicity, and integrating factors of nonlinear ordinary differential equations ⋮ Another look at the complex dilatation ⋮ Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups ⋮ Equivalence of variational problems of higher order ⋮ The invariant functions and invariant-image conditions of the rational Bézier triangles ⋮ Variational problems for Fefferman hypersurface measure and volume-preserving CR invariants ⋮ The Lie group in infinite dimension ⋮ Feedback differential invariants ⋮ Cartan's structure of symmetry pseudo-group and coverings for the \(r\)-th modified dispersionless Kadomtsev-Petviashvili equation ⋮ Differential equations and conformal geometry ⋮ Three snippets of curve evolution theory in computer vision ⋮ On the genesis of the Cartan-Kähler theory ⋮ On the 7th order ODE with submaximal symmetry ⋮ \(\mathrm{GL}(2,\mathbb R)\) geometry of ODEs ⋮ On the stability of Crandall gyropendulum ⋮ Algorithmic symmetry classification with invariance ⋮ Equivalence problem and integrability of the Riccati equations ⋮ On the existence of generalized unicorns on surfaces ⋮ Special conformal groups of a Riemannian manifold and Lie point symmetries of the nonlinear Poisson equation ⋮ Locally homogeneous rigid geometric structures on surfaces ⋮ Symmetry group classification for general Burgers equation ⋮ Recursive moving frames for Lie pseudo-groups ⋮ Hamiltonian evolution of curves in classical affine geometries ⋮ A symmetry classification for a class of \((2+1)\)-nonlinear wave equation ⋮ An extension of Cartan's method of equivalence to immersions. I: Necessary conditions ⋮ Differential invariant algebras of Lie pseudo-groups ⋮ Élie Cartan's geometrical vision or how to avoid expression swell ⋮ Solvable structures associated to the nonsolvable symmetry algebra \(\mathfrak{sl}(2,\mathbb{R})\) ⋮ Differential invariants of a Lie group action: syzygies on a generating set ⋮ Ordinary differential equations described by their Lie symmetry algebra ⋮ The four-dimensional Martínez Alonso-Shabat equation: differential coverings and recursion operators ⋮ Point equivalence of second-order ODEs: maximal invariant classification order ⋮ Differential invariants of surfaces ⋮ Conservation and balance laws in linear elasticity of grade three ⋮ Web geometry of a system of first-order autonomous ordinary differential equations ⋮ Computing representations for radicals of finitely generated differential ideals ⋮ Rotational symmetries of crystals with defects ⋮ Observer-based Hamiltonian identification for quantum systems ⋮ New classification techniques for ordinary differential equations ⋮ Differential systems with Fuchsian linear part: correction and linearization, normal forms and multiple orthogonal polynomials ⋮ New forms of extended Kalman filter via transversal linearization and applications to structural system identification ⋮ The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors ⋮ Differential invariants for systems of linear hyperbolic equations ⋮ Two approaches to the calculation of approximate symmetry of Ostrovsky equation with small parameter ⋮ Approximate Q-conditional symmetries of partial differential equations ⋮ A frame based approach to computing symmetries with non-trivial isotropy groups ⋮ Teleparallel geometry with a single affine symmetry ⋮ Geometric characterization of continuously defective elastic crystals ⋮ Prime ends in the Heisenberg group $\mathbb{H}_{1}$ and the boundary behavior of quasiconformal mappings ⋮ Matrix representations of third order jet groups ⋮ Unnamed Item ⋮ Building New Einstein Spaces by Deforming Symmetric Einstein Spaces ⋮ An Invitation to Quasihomogeneous Rigid Geometric Structures ⋮ Equi-affine differential invariants for invariant feature point detection ⋮ In search of a new economic model determined by logistic growth ⋮ Symmetries of stochastic differential equations: A geometric approach ⋮ Nerve pulse propagation in biological membranes — Solitons and other invariant solutions ⋮ Unnamed Item ⋮ Schwarz triangle functions and duality for certain parameters of the generalised Chazy equation ⋮ Exhaustive Classification of the Invariant Solutions for a Specific Nonlinear Model Describing Near Planar and Marginally Long-Wave Unstable Interfaces for Phase Transition ⋮ Unnamed Item ⋮ APPLICATION OF CARTAN’S EQUIVALENCE METHOD TO DISTRIBUTION OF PLANES ⋮ Differentiall $ {e} $-structures for equivalences of $ 2 $-nondegenerate Levi rank $ 1 $ hypersurfaces $ M_5 ⊂ \mathbb{C} $ ⋮ On Computing Linearizing Coordinates From Symmetry Algebra ⋮ Easy composition of symbolic computation software ⋮ Symbolic integration at compile time in finite element methods ⋮ On the complete integrability and linearization of nonlinear ordinary differential equations. II. Third-order equations ⋮ Computer Algebra Algorithms for Control Related Tests of Implicit Dynamic Systems ⋮ The $\beta$-Delaunay tessellation III: Kendall's problem and limit theorems in high dimensions ⋮ A deceptively simple generalization ⋮ Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny–Lin equation ⋮ Symmetry classification of scalar Ito equations with multiplicative noise ⋮ Sur le problème d’équivalence de Cartan ⋮ Approximate symmetry analysis of nonlinear Rayleigh-wave equation ⋮ Applications of Signatures Curves to Characterize Melanomas and Moles ⋮ The Cartan algorithm in five dimensions ⋮ Geometry of the curved traversable wormholes of (3 + 1)-dimensional spacetime metric ⋮ Exact Linearization and Invariant Solutions of the Generalized Burgers Equation with Linear Damping and Variable Viscosity ⋮ Unnamed Item ⋮ W-symmetries of Ito stochastic differential equations ⋮ Scalar polynomial curvature invariants in the context of the Cartan–Karlhede algorithm ⋮ Affine tensors in mechanics of freely falling particles and rigid bodies ⋮ Chaos in Cartan foliations ⋮ Symmetry and equivalence in teleparallel gravity ⋮ De Donder Construction for Higher Jets ⋮ A Kinematics of Defects in Solid Crystals ⋮ On the commutator of ${\mathcal{C}^{\infty}}$ -symmetries and the reduction of Euler–Lagrange equations ⋮ The classifying Lie algebroid of a geometric structure I: Classes of coframes ⋮ Symmetries and Large Time Asymptotics of Compressible Euler Flows with Damping ⋮ Equivalence of Third‐Order Ordinary Differential Equations to Chazy Equations I–XIII ⋮ Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces ⋮ Differential invariants of Kundt waves ⋮ Locally homogeneous Kundt triples and CSI metrics ⋮ Observer-based invariants for cosmological models ⋮ A note on the period function for certain planar vector fields ⋮ Differential invariants of Kundt spacetimes ⋮ Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems ⋮ Nonlinear Galilei-invariant PDEs with infinite-dimensional Lie symmetry ⋮ Transvectants, modular forms, and the Heisenberg algebra. ⋮ Rankin-Cohen brackets and invariant theory ⋮ Poisson brackets associated to the conformal geometry of curves ⋮ Integrability aspects of a Schwarzian PDE ⋮ Grassmannian spectral shooting ⋮ Equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds ⋮ Integration of the stochastic logistic equation via symmetry analysis ⋮ Symmetry and integrability for stochastic differential equations ⋮ Triangular decomposition of semi-algebraic systems ⋮ On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations ⋮ Homogeneous algebraic distributions ⋮ Differential Equations in Algebras ⋮ Unnamed Item ⋮ Recent advances in symmetry of stochastic differential equations ⋮ A Normal Form for Systems of Implicit Ordinary Differential Equations ⋮ Unnamed Item ⋮ Orbit Computation for Atomically Generated Subgroups of Isometries of $\mathbb{Z}^n$ ⋮ Differential Signatures of Algebraic Curves ⋮ The theory of differential invariants and KDV hamiltonian evolutions ⋮ Unnamed Item ⋮ Invariant tracking ⋮ Tetrahedron maps and symmetries of three dimensional integrable discrete equations ⋮ CONSERVATION LAWS AND SYMMETRY ANALYSIS OF (1+1)-DIMENSIONAL SAWADA-KOTERA EQUATION ⋮ Quantifying wall turbulence via a symmetry approach: a Lie group theory ⋮ SYMMETRY CLASSIFICATION OF NEWTONIAN INCOMPRESSIBLEFLUID’S EQUATIONS FLOW IN TURBULENT BOUNDARY LAYERS ⋮ Оптимальные системы одномерных подалгебр алгебры симметрий трeхмерных уравнений математической теории пластичности ⋮ Geometry of rank 2 distributions with nonzero Wilczynski invariants* ⋮ Simple and collective twisted symmetries ⋮ On Lie-point symmetries for Ito stochastic differential equations ⋮ Teleparallel geometries not characterized by their scalar polynomial torsion invariants ⋮ Exact solutions of Klein–Gordon equations in external electromagnetic fields on 3D de Sitter background ⋮ Symmetry-Preserving Finite Element Schemes: An Introductory Investigation ⋮ On differential invariants of parabolic surfaces ⋮ Unnamed Item ⋮ Sum of squares manifolds: The expressibility of the Laplace-Beltrami operator on pseudo-Riemannian manifolds as a sum of squares of vector fields ⋮ Connection and curvature in crystals with non-constant dislocation density ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Symmetry Reduction, Contact Geometry, and Partial Feedback Linearization ⋮ A model of trophodynamics ⋮ Symmetry reduction of ordinary finite difference equations using moving frames ⋮ Dynamically equivalent ΛCDMequations with underlying Bianchi Type geometry ⋮ Symmetry properties, similarity reduction and exact solutions of fractional Boussinesq equation ⋮ First integrals and parametric solutions of third-order ODEs admitting $ {\mathfrak{sl}(2, \mathbb{R})} $ ⋮ Second-order delay ordinary differential equations, their symmetries and application to a traffic problem ⋮ Classification of Lie Subalgebras up to an Inner Automorphism ⋮ Projective invariants of images ⋮ Lie-Cartan differential invariants and Poincaré-Moser normal forms: Conflunces ⋮ Invariants: Computation and Applications ⋮ On uniqueness of submaximally symmetric vector ordinary differential equations of C-class ⋮ Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit ⋮ Normal forms of second-order ordinary differential equations \(y_{xx}=J(x,y,y_x)\) under fibre-preserving maps ⋮ Symmetries of Ricci flows ⋮ Spatially homogeneous teleparallel gravity: Bianchi I ⋮ Integrability of quaternion-Kähler symmetric spaces ⋮ Rigid biholomorphic equivalences of rigid \(\mathfrak{C}_{2 , 1}\) hypersurfaces \(M^5 \subset \mathbb{C}^3\) ⋮ Jet spaces over Carnot groups ⋮ Differential invariants of Camassa-Holm equation ⋮ Exact hierarchical reductions of dynamical models via linear transformations ⋮ Holomorphic projective connections on surfaces ⋮ On the integration of Ito equations with a random or a W-symmetry ⋮ Homogeneous CR and Para-CR structures in dimensions 5 and 3 ⋮ Generalization of Noether theorem and action principle for non-Lagrangian theories ⋮ Generalized Solvable Structures Associated to Symmetry Algebras Isomorphic to $$\mathfrak {gl}(2,\mathbb {R}) \ltimes \mathbb {R}$$ ⋮ A Geometric Framework to Compare PDEs and Classical Field Theories ⋮ Normal forms, moving frames, and differential invariants for nondegenerate hypersurfaces in \(\mathbb{C}^2\) ⋮ Modular forms via invariant theory ⋮ Revisiting Kepler: new symmetries of an old problem ⋮ From second-order differential geometry to stochastic geometric mechanics ⋮ On the integrability of GL(2,ℝ)‐invariant fourth‐order ordinary differential equations ⋮ Tulczyjew’s triplet with an Ehresmann connection I: Trivialization and reduction ⋮ On the total CR twist of transversal curves in the 3-sphere ⋮ Variational λ‐symmetries and exact solutions to Euler‐Lagrange equations lacking standard symmetries ⋮ Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation ⋮ Exact solutions to a family of position‐dependent mass damped oscillators from variational λ‐symmetries ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Fast differential eleminination in C: The CDiffElim environment ⋮ Recognizing the symmetry type of O. D. E. s ⋮ Integrable equations arising from motions of plane curves ⋮ Special issue: Themes in geometric integration ⋮ Time symmetry and high-order Magnus methods ⋮ Quadrature methods based on the Cayley transform ⋮ A classification of locally homogeneous connections on 2-dimensional manifolds ⋮ Maximal degree variational principles and Liouville dynamics ⋮ Equivalence conditions and invariants for the general form of Burgers' equations ⋮ An illustrative application of the Lie symmetries in the context of first-order mechanical systems: Hathaway's circular pursuit problem ⋮ Modeling the combined parameter for incipient motion from the force balance on a single proud grain ⋮ A modified formal Lagrangian formulation for general differential equations ⋮ Prolonged analytic connected group actions are generically free ⋮ Computer algebra methods for implicit dynamic systems and applications ⋮ Some new exact solutions of \((3+1)\)-dimensional Burgers system via Lie symmetry analysis ⋮ On curves with the Poritsky property ⋮ A consistent approach to approximate Lie symmetries of differential equations ⋮ Differential invariants of Einstein-Weyl structures in 3D ⋮ A full three dimensional numerical simulation of the sediment transport and the scouring at a rectangular obstacle ⋮ Numerical simulation of the temporal evolution of a three dimensional barchanoid dune and the corresponding sediment dynamics ⋮ Differential invariants ⋮ Lie group analysis and Riemann problems for a \(2\times 2\) system of balance laws ⋮ Symmetry gaps for higher order ordinary differential equations ⋮ Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations ⋮ Sasakian structure associated with a second-order ODE and Hamiltonian dynamical systems ⋮ Generation and identification of ordinary differential equations of maximal symmetry algebra ⋮ Differential geometric aspects of causal structures ⋮ Linearizable second order Monge-Ampère equations ⋮ Joint differential invariants of binary and ternary forms ⋮ Equivalence transformations of the Euler-Bernoulli equation ⋮ Equivalence transformations of quasilinear first order systems and reduction to autonomous and homogeneous form ⋮ A remark on nonlinear accessibility conditions and infinite prolongations. ⋮ Euclidean signature curves ⋮ Explicit absolute parallelism for 2-nondegenerate real hypersurfaces \(M^5 \subset \mathbb{C}^3\) of constant Levi rank 1 ⋮ Explicit expression of Cartan's connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere ⋮ Contact integrable extensions and differential coverings for the generalized \((2 + 1)\)-dimensional dispersionless Dym equation ⋮ On covariant realizations of the Poincaré group \(P(1,3)\) ⋮ Differential invariants of a generalized variable-coefficient Gardner equation ⋮ Inequivalent Goldstone hierarchies for spontaneously broken spacetime symmetries ⋮ Classification of jets of surfaces in projective 3-space via central projection ⋮ Exceptionally simple PDE ⋮ Order preserving contact transformations and dynamical symmetries of scalar and coupled Riccati and Abel chains ⋮ Invariance of second order ordinary differential equations under two-dimensional affine subalgebras of Ermakov-Pinney Lie algebra ⋮ Subriemannian metric induced by single-input locally accessible control-affine systems ⋮ Symmetric (2,3,5) distributions, an interesting ODE of 7th order and Plebański metric ⋮ Higher symmetries of symplectic Dirac operator ⋮ Structure of Lie point and variational symmetry algebras for a class of odes ⋮ Group foliation of finite difference equations ⋮ Invariant characterization of third-order ordinary differential equations \(u= f(x, u, u', u)\) with five-dimensional point symmetry group ⋮ Some results on equivalence groups ⋮ Lie symmetry analysis of the two-dimensional generalized Kuramoto-Sivashinsky equation ⋮ Differential invariants: Theorem of commutativity. ⋮ On affine Sawada-Kotera equation. ⋮ A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach ⋮ Renormalization group derivation of phase equations ⋮ Feature matching and heat flow in centro-affine geometry ⋮ Equivalence and identifiability analysis of uncontrolled nonlinear dynamical systems. ⋮ Homogeneous Levi non-degenerate hypersurfaces in \(\mathbb{C}^3\) ⋮ Motions of curves in similarity geometries and Burgers-mKdV hierarchies ⋮ Solutions of second-order PDEs with first-order quotients ⋮ Lie symmetry analysis and conservation law of variable-coefficient Davey-Stewartson equation ⋮ Control of nonlinear distributed parameter systems using generalized invariants ⋮ Differential invariants of classical groups ⋮ Differential equations in a tangent category. I: Complete vector fields, flows, and exponentials ⋮ Lie-point symmetries preserved by derivative ⋮ Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations ⋮ Growth and form, Lie algebras and special functions ⋮ Contact manifolds, Lagrangian Grassmannians and PDEs ⋮ Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations ⋮ Unbendable rational curves of Goursat type and Cartan type ⋮ Automatic solution of jigsaw puzzles ⋮ Some variational principles associated with ODEs of maximal symmetry. II: The general case ⋮ Recursive moving frames ⋮ Co-calibrated \(G_2\) structure from cuspidal cubics ⋮ Comprehensive analysis of the symmetries and conservation laws of the geodesic equations for a particular string inspired FRLW solution ⋮ Linear gradient structures and discrete gradient methods for conservative/dissipative differential-algebraic equations ⋮ Geometrical structure of two-dimensional crystals with non-constant dislocation density ⋮ Approximate symmetry analysis of a class of perturbed nonlinear reaction-diffusion equations ⋮ Point and contact equivalence groupoids of two-dimensional quasilinear hyperbolic equations ⋮ Ordinary differential equations invariant under two-variable Möbius transformations ⋮ Invariants of surfaces in three-dimensional affine geometry ⋮ Consistent approximate Q-conditional symmetries of PDEs: application to a hyperbolic reaction-diffusion-convection equation ⋮ Symmetry-based algorithms for invertible mappings of polynomially nonlinear PDE to linear PDE ⋮ Non-congruent non-degenerate curves with identical signatures ⋮ Exact solutions of the two-dimensional Cattaneo model using Lie symmetry transformations ⋮ Preliminary group classification and some exact solutions of the 2-Hessian equation ⋮ Almost all Finsler metrics have infinite dimensional holonomy group ⋮ The Cayley cubic and differential equations ⋮ The geometry of marked contact Engel structures ⋮ Convergent normal form for five dimensional totally nondegenerate CR manifolds in \(\mathbb{C}^4\) ⋮ Reducing \(y=F(x,y,y')\) to first order. ⋮ Minimal functional bases for elasticity tensor symmetry classes ⋮ Para-Kähler-Einstein \(4\)-manifolds and non-integrable twistor distributions ⋮ On convergent Poincaré-Moser reduction for Levi degenerate embedded 5-dimensional CR manifolds ⋮ Michel theory of symmetry breaking and gauge theories ⋮ Hamilton equations for elasticae in the Euclidean 3-space ⋮ High order Runge-Kutta methods on manifolds ⋮ Contact Lie algebras of vector fields on the plane ⋮ On the Poincaré problem ⋮ Specialisation of the Galois groupoid of a vector field ⋮ A new method to detect projective equivalences and symmetries of rational \(3 D\) curves ⋮ Computer algebra solving second order ODEs using symmetry methods ⋮ The geometry of the equation \(y=f(x,y,y',y)\) ⋮ Learning-based non-rigid video depth estimation using invariants to generalized bas-relief transformations ⋮ Complexity theory for Lie-group solvers ⋮ Some recent developments on Lie symmetry analysis of stochastic differential equations