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.
Extended symmetry analysis of generalized Burgers equations
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abstract
Using advanced classification techniques, we carry out the extended symmetry analysis of the class of generalized Burgers equations of the form $u_t+uu_x+f(t,x)u_{xx}=0$. This enhances all the previous results on symmetries of these equations and includes the description of admissible transformations, Lie symmetries, Lie and nonclassical reductions, conservation laws, potential admissible transformations and potential symmetries. The study is based on the fact that the class is normalized, and its equivalence group is finite-dimensional.
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Extended symmetry analysis of two-dimensional degenerate Burgers equation
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.