Symmetry group classification for general Burger's equation

Details Symmetry group classification for general Burger's equation Symmetry group classification for general Burger's equation

2009-08-26

arxiv.org/abs/0908.3757v1

Communications in Nonlinear Science and Numerical Simulations, 2009

Mathematics

Differential Geometry

9 pages

Scientific paper

10.1016/j.cnsns.2009.09.031

The present paper solves the problem of the group classification of the general Burgers' equation $u_t=f(x,u)u_x^2+g(x,u)u_{xx}$, where $f$ and $g$ are arbitrary smooth functions of the variable $x$ and $u$, by using Lie method. The paper is one of the few applications of an algebraic approach to the problem of group classification: the method of preliminary group classification. A number of new interesting nonlinear invariant models which have nontrivial invariance algebras are obtained. The result of the work is a wide class of equations summarized in table form.

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