Abstract

Group Classification of Quasilinear Evolution Equations

V.Lagno (State Pedagogical University, Poltava, Ukraine)

e-mail: laggo@poltava.bank.gov.ua

The present talk contain complete solution of the problem of the group classification of quasi-linear evolution equations of most general form. Here we make use of an approach, proposed by [1]. We have proved, in particular, that the above class contains no nonlinear equations whose invariance algebra has dimension more than five. The principal result of group classification is the following: there are two, five, thirty--four, thirty--five and five inequivalent equations admitting one-, two-, three-, four- and five dimensional invariance algebras. [1] Zhdanov R.Z. and Lahno V.I. Group classification of heat conductivity equations with a nonlinear sourse, J. Phys. A: Math. Gen., 1999, V.32, 7405-7418.

Section : 12