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Group analysis of a class of nonlinear Kolmogorov equations

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arxiv 1509.04481 v4 pith:3TCLCKC7 submitted 2015-09-15 math-ph math.APmath.MPnlin.SI

Olena Vaneeva , Yuri Karadzhov , Christodoulos Sophocleous This is my paper · ORCID
classification math-phmath.APmath.MPnlin.SI
keywords equationsclasscoefficientsequivalencegroupkolmogorovnonlinearachieved
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A class of (1+2)-dimensional diffusion-convection equations (nonlinear Kolmogorov equations) with time-dependent coefficients is studied with Lie symmetry point of view. The complete group classification is achieved using a gauging of arbitrary elements (i.e. via reducing the number of variable coefficients) with the application of equivalence transformations. Two possible gaugings are discussed in detail in order to show how equivalence groups serve in making the optimal choice.

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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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