Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations
From MaRDI portal
Publication:2213869
DOI10.1016/j.cnsns.2020.105419zbMath1453.35011arXiv2002.08939OpenAlexW3036145869MaRDI QIDQ2213869
Roman O. Popovych, Alexander Bihlo, Olena O. Vaneeva
Publication date: 3 December 2020
Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2002.08939
Semilinear elliptic equations (35J61) Symmetries, invariants, etc. in context of PDEs (35B06) Second-order semilinear hyperbolic equations (35L71)
Related Items (9)
Mapping method of group classification ⋮ Two approximate symmetry frameworks for nonlinear partial differential equations with a small parameter: Comparisons, relations, approximate solutions ⋮ Extended symmetry analysis of remarkable (1+2)-dimensional Fokker–Planck equation ⋮ Abelian Lie symmetry algebras of two‐dimensional quasilinear evolution equations ⋮ Lie reductions and exact solutions of generalized Kawahara equations ⋮ Lie symmetries of two-dimensional shallow water equations with variable bottom topography ⋮ Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations ⋮ Equivalence transformations of a fifth-order partial differential equation with variable-coefficients ⋮ Point and contact equivalence groupoids of two-dimensional quasilinear hyperbolic equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities
- Enhanced preliminary group classification of a class of generalized diffusion equations
- Group-theoretical analysis of variable coefficient nonlinear telegraph equations
- Group analysis of variable coefficient diffusion-convection equations. I: Enhanced group classification
- Group classification of linear evolution equations
- Group classification of quasilinear elliptic-type equations. II. Invariance under solvable Lie algebras
- Symmetry classification and optimal systems of a non-linear wave equation
- Enhanced group analysis and conservation laws of variable coefficient reaction-diffusion equations with power nonlinearities
- Enhanced group classification of gardner equations with time-dependent coefficients
- Admissible transformations and normalized classes of nonlinear Schrödinger equations
- Preliminary group classification for the nonlinear wave equation \(u_{tt}=f(x,u)u_{xx}+g(x,u)\)
- Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source
- Applications of symmetry methods to partial differential equations
- Nonlocal symmetries. Heuristic approach
- Algebraic method for group classification of \((1+1)\)-dimensional linear Schrödinger equations
- Classifying evolution equations.
- Group classification of linear fourth-order evolution equations
- Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations
- Functional separable solutions of nonlinear convection-diffusion equations with variable coefficients
- Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity
- Conservation laws and potential symmetries of linear parabolic equations
- Group classification and exact solutions of nonlinear wave equations
- Automorphisms of real Lie algebras of dimension five or less
- Complete group classification of a class of nonlinear wave equations
- New results on group classification of nonlinear diffusion–convection equations
- On invariant solutions of the equation of non-linear heat conduction with a source
- Group classification of nonlinear wave equations
- Framework for nonlocally related partial differential equation systems and nonlocal symmetries: Extension, simplification, and examples
- Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations
- Group classification of quasilinear elliptic-type equations. I. Invariance with respect to Lie algebras with nontrivial Levi decomposition
- Preliminary group classification of a class of fourth-order evolution equations
- On invariance properties of the wave equation
- On form-preserving point transformations of partial differential equations
- Preliminary group classification of equations v t t=f (x,v x)v x x+g(x,v x)
- Discrete point symmetries of ordinary differential equations
- Orthogonal and non-orthogonal separation of variables in the wave equation utt-uxx+V(x)u=0utt-uxx+V(x)u=0
- Realizations of real low-dimensional Lie algebras
- Equivalence groupoid of a class of variable coefficient Korteweg–de Vries equations
- Symmetries of variable coefficient Korteweg–de Vries equations
- How to construct the discrete symmetries of partial differential equations
- Symmetry classification of KdV-type nonlinear evolution equations
- Symmetry classes of variable coefficient nonlinear Schrodinger equations
- CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
- Generalization of the Equivalence Transformations
- Equivalence groupoid of a class of general Burgers-Korteweg-de Vries equations with space-dependent coefficients
- Symmetry reductions and new functional separable solutions of nonlinear Klein–Gordon and telegraph type equations
- Kinematical invariance groups of the 3d Schrödinger equations with position dependent masses
- Group analysis of general Burgers–Korteweg–de Vries equations
- Symmetry-Preserving Numerical Schemes
- Symmetries and differential equations
- The structure of Lie algebras and the classification problem for partial differential equations
This page was built for publication: Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations
