Conservation laws by symmetries and adjoint symmetries

Wen-Xiu Ma

doi:10.3934/dcdss.2018044

Article Contents

2018, Volume 11, Issue 4: 707-721. Doi: 10.3934/dcdss.2018044

This issue Previous Article A study of bifurcation parameters in travelling wave solutions of a damped forced Korteweg de Vries-Kuramoto Sivashinsky type equation Next Article Characterization of partial Hamiltonian operators and related first integrals

Conservation laws by symmetries and adjoint symmetries

Wen-Xiu Ma^1,2,3,4, ,

1.
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
2.
Department of Mathematics and Statistics, University of South Florida Tampa, FL 33620, USA
3.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
4.
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

* Corresponding author: Wen-Xiu Ma
* Corresponding author: Wen-Xiu Ma

Received: January 2017

Published: August 2018

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Abstract

Conservation laws are fomulated for systems of differential equations by using symmetries and adjoint symmetries, and an application to systems of evolution equations is made, together with illustrative examples. The formulation does not require the existence of a Lagrangian for a given system, and the presented examples include computations of conserved densities for the heat equation, Burgers' equation and the Korteweg-de Vries equation.

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Mathematics Subject Classification: 70S10, 37K05, 35Q51.

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