Determination of approximate nonlinear self-adjointenss and approximate conservation law
Abstract
Approximate nonlinear self-adjointness is an effective method to construct approximate conservation law of perturbed partial differential equations (PDEs). In this paper, we study the relations between approximate nonlinear self-adjointness of perturbed PDEs and nonlinear self-adjointness of the corresponding unperturbed PDEs, and consequently provide a simple approach to discriminate approximate nonlinear self-adjointness of perturbed PDEs. Moreover, a succinct approximate conservation law formula by virtue of the known conservation law of the unperturbed PDEs is given in an explicit form. As an application, we classify a class of perturbed wave equations to be approximate nonlinear self-adjointness and construct the general approximate conservation laws formulae. The specific examples demonstrate that approximate nonlinear self-adjointness can generate new approximate conservation laws.
Keywords
Cite
@article{arxiv.1301.4534,
title = {Determination of approximate nonlinear self-adjointenss and approximate conservation law},
author = {Zhi-Yong Zhang},
journal= {arXiv preprint arXiv:1301.4534},
year = {2015}
}
Comments
Overlap the original version