Symmetry classification of third-order nonlinear evolution equations. Part I: Semi-simple algebras

Abstract

We give a complete point-symmetry classification of all third-order evolution equations of the form $u_t=F(t,x,u,u_x,u_{xx})u_{xxx}+G(t,x,u,u_x,u_{xx})$ which admit semi-simple symmetry algebras and extensions of these semi-simple Lie algebras by solvable Lie algebras. The methods we employ are extensions and refinements of previous techniques which have been used in such classifications.

53 pages

References in corpus (1)

• Symmetry classification of KdV-type nonlinear evolution equations

Cited by in corpus (2)

• Linearizability for third order evolution equations
• Lie group analysis of a generalized Krichever-Novikov differential-difference equation