Invariant sets of evolution equations

DOI10.1016/0362-546X(92)90219-5zbMath0812.35052OpenAlexW1972984003MaRDI QIDQ4032212

Oleg V. Kaptsov

Publication date: 1 April 1993

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(92)90219-5

zbMATH Keywords

invariant sets\(xt\)-method

Mathematics Subject Classification ID

Invariance and symmetry properties for PDEs on manifolds (58J70) Initial value problems for linear higher-order PDEs (35G10) Overdetermined systems of PDEs with variable coefficients (35N10) Other special methods applied to PDEs (35A25) Higher-order parabolic equations (35K25)

Related Items (16)

Conditional Lie-Bäcklund symmetries and differential constraints for inhomogeneous nonlinear diffusion equations due to linear determining equations ⋮ Conditional symmetry and spectrum of the one-dimensional Schrödinger equation ⋮ An upper order bound of the invariant manifold in Lax pairs of a nonlinear evolution partial differential equation ⋮ Quasilinear heat equations with first-order sign-invariants and new explicit solutions ⋮ Generalized conditional symmetries of evolution equations ⋮ Conditional Lie Bäcklund symmetries and solutions to (n+1)-dimensional nonlinear diffusion equations ⋮ Evolution equations, invariant surface conditions and functional separation of variables ⋮ A multidimensional superposition principle: classical solitons. III ⋮ Second-order conditional Lie-Bäcklund symmetry and differential constraint of radially symmetric diffusion system ⋮ The functional separation method based on the singular manifold method ⋮ A supersymmetric second modified KdV equation ⋮ Third-order conditional Lie-Bäcklund symmetries of nonlinear reaction-diffusion equations ⋮ New explicit solutions of quasilinear heat equations with general first-order sign-invariants ⋮ A multidimensional superposition principle: classical solitons. I ⋮ Separation of variables of a generalized porous medium equation with nonlinear source. ⋮ Maximal dimension of invariant subspaces admitted by nonlinear vector differential operators

Cites Work

• New solutions of two-dimensional stationary Euler equations
• Classification of evolution equations by conservation laws
• Spectral theory for the periodic sine-Gordon equation: A concrete viewpoint
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