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Algebraic method for finding equivalence groups

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arxiv 1503.06487 v2 pith:F73OY6W2 submitted 2015-03-22 math-ph math.APmath.MP

Alexander Bihlo , Elsa Dos Santos Cardoso-Bihlo , Roman O. Popovych This is my paper · ORCID
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keywords methodequivalencegroupcompletealgebraalgebraicclassequations
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The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the corresponding equivalence algebra. Two versions of the method are presented, where the first involves the automorphism group of this algebra and the second is based on a list of its megaideals. We illustrate the megaideal-based version of the method with the computation of the complete equivalence group of a class of nonlinear wave equations with applications in nonlinear elasticity.

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  1. Extended symmetry analysis of two-dimensional degenerate Burgers equation

    math.AP 2019-08 accept novelty 7.0 of 10

    For the degenerate Burgers equation u_t + u u_x - u_yy = 0, all generalized symmetries reduce to Lie symmetries, and conservation laws are in one-to-one correspondence with solutions of the backward heat equation.

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