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.
Sufficient set of integrability conditions of an orthonomic system
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abstract
Every orthonomic system of partial differential equations is known to possess a finite number of integrability conditions sufficient to ensure the validity of all. Herewith we offer an efficient algorithm to construct a sufficient set of integrability conditions free of redundancies.
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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.