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Solutions of Two Nonlinear Evolution Equations Using Lie Symmetry and Simplest Equation Methods

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Abstract

In this paper, we study two nonlinear evolution partial differential equations, namely, a modified Camassa–Holm–Degasperis–Procesi equation and the generalized Korteweg–de Vries equation with two power law nonlinearities. For the first time, the Lie symmetry method along with the simplest equation method is used to construct exact solutions for these two equations.

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Authors and Affiliations

  1. Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho, 2735, Republic of South Africa

    Isaiah Elvis Mhlanga & Chaudry Masood Khalique

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  1. Isaiah Elvis Mhlanga
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  2. Chaudry Masood Khalique
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Correspondence to Chaudry Masood Khalique.

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Mhlanga, I.E., Khalique, C.M. Solutions of Two Nonlinear Evolution Equations Using Lie Symmetry and Simplest Equation Methods. Mediterr. J. Math. 11, 487–496 (2014). https://doi.org/10.1007/s00009-013-0309-6

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  • DOI: https://doi.org/10.1007/s00009-013-0309-6

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