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Generalised conservation laws, reductions and exact solutions of the \(K(m,n)\) equations via double reduction theory

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Abstract

In this article, we present the general form of conservation laws for the nonlinear Rosenau–Hyman compacton K(m, n) equations using multiplier’s approach. General formulas for some new conservation laws are established for the K(m, n) equations. We describe three different cases where Lie symmetries are associated with these generalised conservation laws. The double reduction theory is utilised to construct some new reductions and exact solutions for different values of m and n.

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Authors and Affiliations

  1. Department of Mathematics, School of Science and Engineering, Lahore University of Management Sciences, Lahore Cantt,     54792, Pakistan

    A Iqbal & I Naeem

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  1. A Iqbal
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  2. I Naeem
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Correspondence to I Naeem.

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Iqbal, A., Naeem, I. Generalised conservation laws, reductions and exact solutions of the \(K(m,n)\) equations via double reduction theory. Pramana - J Phys 95, 30 (2021). https://doi.org/10.1007/s12043-020-02071-z

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  • DOI: https://doi.org/10.1007/s12043-020-02071-z

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