Conservation laws for self-adjoint ?rst order evolution equations

Details Conservation laws for self-adjoint ?rst order evolution equations Conservation laws for self-adjoint ?rst order evolution equations

2010-02-21

arxiv.org/abs/1002.3986v2

Physics

Mathematical Physics

This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physics

Scientific paper

In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.

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