Conservation laws for self-adjoint first order evolution equations
Mathematical Physics
2018-11-21 v2 math.MP
Abstract
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.
Cite
@article{arxiv.1002.3986,
title = {Conservation laws for self-adjoint first order evolution equations},
author = {Igor Leite Freire},
journal= {arXiv preprint arXiv:1002.3986},
year = {2018}
}
Comments
This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physics