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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:

35Q53 KdV equations (Korteweg-de Vries equations)
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
58J70 Invariance and symmetry properties for PDEs on manifolds
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics
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