Double reduction of the Gibbons-Tsarev equation using admitted Lie point symmetries and associated conservation laws
نویسندگان
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 Mathematical Sciences and Computing, Faculty of Natural Sciences, Walter Sisulu University, Private Bag X1, Mthatha 5117, Republic of South Africa
3 Department of Mathematics, Dammam Community College, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
4 College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Rawalpindi, 46070, Pakistan
doi
10.22075/ijnaa.2022.25829.3136چکیده
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.
