Reduction operators and exact solutions of generalized Burgers equations

Oleksandr A. Pocheketa; Roman O. Popovych

Reduction operators and exact solutions of generalized Burgers equations

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arxiv 1112.6394 v1 pith:IMPJDIKZ submitted 2011-12-29 math-ph math.APmath.MP

Oleksandr A. Pocheketa , Roman O. Popovych This is my paper · ORCID

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keywords equationsburgersgeneralizedoperatorsreductionsolutionsconnectiondiffusion

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Reduction operators of generalized Burgers equations are studied. A connection between these equations and potential fast diffusion equations with power nonlinearity -1 via reduction operators is established. Exact solutions of generalized Burgers equations are constructed using this connection and known solutions of the constant-coefficient potential fast diffusion equation.

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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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