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

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

2010-10-05

arxiv.org/abs/1010.0880v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

53 pages

Scientific paper

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.

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