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