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Symmetry group classification for general Burgers equation. (English) Zbl 1222.35195
Summary: 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 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 on its Lie algebra 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.
35Q60PDEs in connection with optics and electromagnetic theory
35K55Nonlinear parabolic equations
35A30Geometric theory for PDE, characteristics, transformations
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