R Zhdanov and V Lahno 2007 J. Phys. A: Math. Theor. 40 5083 doi:10.1088/1751-8113/40/19/010
R Zhdanov1 and V Lahno2
Show affiliationsIn this paper, we consider the problem of group classification of the generic second-order evolution equation in one spatial variable. We construct all inequivalent evolution equations whose invariance groups are either semi-simple or semi-direct products of semi-simple and solvable Lie groups. The obtained lists of invariant equations contain both already known equations and the broad classes of new evolution equations possessing nontrivial Lie symmetry.
35G10 Initial value problems for linear higher-order PDE, linear evolution equations
22E46 Semisimple Lie groups and their representations
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
Issue 19 (11 May 2007)
Received 2 January 2007, in final form 26 March 2007
Published 24 April 2007
R Zhdanov and V Lahno 2007 J. Phys. A: Math. Theor. 40 5083
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