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Numerical soliton solution of the Kaup-Kupershmidt equation. (English) Zbl 1231.65195
Summary: The purpose of this paper is to obtain soliton solution of the Kaup-Kupershmidt (KK) equation with initial condition. The most important feature of this method is to obtain the solution without direct transformation. In this paper, the homotopy perturbation method (HPM) is used for obtaining soliton solution of the KK equation. The numerical solutions are compared with the known analytical solutions. The results of numerical examples are presented and only a few terms are required to obtain accurate solutions. Results derived from this method are shown graphically. The authors obtained the one soliton solution for the KK equation by HPM. The numerical results showed that this method is very accurate. The HPM provides a reliable technique that requires less work if compared with the traditional techniques and the method does not also require unjustified assumptions, linearization, discretization or perturbation. The HPM is very easily applied to both differential equations and linear or nonlinear differential systems. The paper describes how the authors obtained one soliton solution for the KK equation by HPM. The numerical results presented show that this method is very accurate.
MSC:
65M99Numerical methods for IVP of PDE
35Q51Soliton-like equations
35Q53KdV-like (Korteweg-de Vries) equations