# American Institute of Mathematical Sciences

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August  2018, 11(4): 707-721. doi: 10.3934/dcdss.2018044

## Conservation laws by symmetries and adjoint symmetries

 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

Received  January 2017 Published  November 2017

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.

Citation: Wen-Xiu Ma. Conservation laws by symmetries and adjoint symmetries. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 707-721. doi: 10.3934/dcdss.2018044
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