Volume 18, Issue 2, June 2011, Pages 279 - 290
Conservation Laws for Self-Adjoint First-Order Evolution Equation
Authors
Igor Leite Freire
Centro de Matemática, Computação e Cognição, Universidade Federal do ABC — UFABC, Rua Santa Adélia, 166, Bairro Bangu, Santo André, São Paulo 09210-170, Brazil,igor.freire@ufabc.edu.br,igor.leite.freire@gmail.com
Received 24 October 2010, Accepted 26 November 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001453How to use a DOI?
- Keywords
- Lie point symmetry; Ibragimov's theorem; conservation laws; inviscid Burgers equation
- Abstract
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.
- Copyright
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Igor Leite Freire PY - 2021 DA - 2021/01/07 TI - Conservation Laws for Self-Adjoint First-Order Evolution Equation JO - Journal of Nonlinear Mathematical Physics SP - 279 EP - 290 VL - 18 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001453 DO - 10.1142/S1402925111001453 ID - Freire2021 ER -