Group classification of the general second-order evolution equation: semi-simple invariance groups

DOI10.1088/1751-8113/40/19/010zbMath1133.35002OpenAlexW1967665325MaRDI QIDQ5293900

V. I. Lahno, Renat Zhdanov

Publication date: 4 July 2007

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1751-8113/40/19/010

zbMATH Keywords

point symmetryone spatial variable

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Abstract parabolic equations (35K90) Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30)

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Lie group classification of the \(N\)-th-order nonlinear evolution equations ⋮ Abelian Lie symmetry algebras of two‐dimensional quasilinear evolution equations ⋮ Symmetry classification of third-order nonlinear evolution equations. I: Semi-simple algebras ⋮ Preliminary group classification of $(2+1)$-dimensional linear ultraparabolic Kolmogorov - Fokker - Planck equations ⋮ Group-theoretical analysis of variable coefficient nonlinear telegraph equations ⋮ On relation between potential and contact symmetries of evolution equations ⋮ Conservation Laws for Self-Adjoint First-Order Evolution Equation ⋮ Admissible transformations and normalized classes of nonlinear Schrödinger equations ⋮ Group classification of differential-difference equations: low-dimensional Lie algebras ⋮ Nonlocal symmetries of evolution equations ⋮ Classification of local and nonlocal symmetries of fourth-order nonlinear evolution equations ⋮ Galilei symmetries of KdV-type nonlinear evolution equations ⋮ Group classification of nonlinear evolution equations: semi-simple groups of contact transformations ⋮ Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source ⋮ Preliminary group classification of a class of fourth-order evolution equations ⋮ Infinite-dimensional symmetries of two-dimensional generalized Burgers equations

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