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Zbl 1222.35195
Symmetry group classification for general Burgers equation.
(English)
[J] Commun. Nonlinear Sci. Numer. Simul. 15, No. 9, 2303-2310 (2010). ISSN 1007-5704

Summary: The present paper solves the problem of the group classification of the general Burgers' equation $u_t=f(x,u)u^2_x+g(x,u)u_{xx}$, where $f$ and $g$ are arbitrary smooth functions of the variable $x$ and $u$, by using the Lie method. The paper is one of the few applications of an algebraic approach to the problem of group classification that is called preliminary group classification. Looking at the adjoint representation of $G_{\cal E}$ on its Lie algebra $\frak g_5$, we will deal with the construction of the optimal system of its one-dimensional subalgebras. The result of the work is a wide class of equations summarized in table form.
MSC 2000:
*35Q60 PDE of electromagnetic theory and optics
35K55 Nonlinear parabolic equations
35A30 Geometric theory for PDE, transformations

Keywords: infinitesimal generator; general Burgers equation; optimal system; preliminarily group classification

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