Double reduction of the Gibbons-Tsarev equation using admitted Lie point symmetries and associated conservation laws

Document Type : Research Paper


1 Department of Mathematical Sciences and Computing, Faculty of Natural Sciences, Walter Sisulu University, Private Bag X1, Mthatha 5117, Republic of South Africa

2 Department of Mathematics, Dammam Community College, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

3 College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Rawalpindi, 46070, Pakistan


In this article, the double reduction method is used to find solutions to a (1+1) nonlinear partial differential equation that arises in the theory of dispersionless integrable systems. Four nontrivial conservation laws of the equation are constructed via the multiplier method, based on a particular form of admitted multipliers. Two of the constructed conservation laws are found to have associated Lie point symmetries and are utilised to construct invariant solutions.


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Volume 13, Issue 2
July 2022
Pages 713-721
  • Receive Date: 07 January 2022
  • Accept Date: 12 April 2022