Nonlinear Evolution Equations and Semi-Simple Lie Algebras (pp.331-362)
Authors: (R. Zhdanov, V. Lahno, C.Z. Qu, BIO-Key International, Eagan, Minnesota, USA, and others)
Abstract: We present the detailed account of our recent results on group classificatio of
nonlinear evolution equations in one spatial variable. In this publication we focus on
nonlinear evolution equations that admit semi-simple Lie algebras. We give exhaustive
description of second-order evolution equations whose symmetry algebras contain
semi-simple subalgebras. The same problem is solved for the class of third-order
quasi-linear (KdV type) evolution equations. We present the exhaustive classificatio
of fourth-order quasi-linear evolution equations invariant under semi-simple Lie algebras.
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