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Conservation laws for self-adjoint first-order evolution equation. (English) Zbl 1219.35228
Summary: We consider the problem on group classification and conservation laws for first-order evolution equations. Subclasses of these general equations which are quasi-self-adjoint and self-adjoint are obtained. By using the recent new conservation theorem due to Ibragimov, conservation laws for equations admiting self-adjoint equations are established. The results are illustrated applying them to the inviscid Burgers equation. In particular an infinite number of new symmetries of this equation are found.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
76M60Symmetry analysis, Lie group and algebra methods (fluid mechanics)
58J70Invariance and symmetry properties
70G65Symmetries, Lie-group and Lie-algebra methods for dynamical systems