Abstract
In this letter, variational homotopy perturbation method (VHPM) has been studied to obtain solitary wave solutions of modified Camassa-Holm and Degasperis-Procesi equations. The results show that the VHPM is suitable for solving nonlinear differential equations with fully nonlinear dispersion term. The travelling wave solution for above equation compared with VIM, HPM, and exact solution. Also, it was shown that the present method is effective, suitable, and reliable for these types of equations.
Highlights
Many varieties of physical, chemical, and biological phenomena can be expressed in terms of nonlinear partial differential equations
It should be remarked that the graph drawn here and approximate solution using variational homotopy perturbation method (VHPM) is in excellent agreement with Homotopy Perturbation Method (HPM) [16] and Variational Iteration Method (VIM) [17]
Figures we show the accurance of VHPM to finding analytical solution of Modified Camassa-Holm and Degasperis-Procesi equations
Summary
Chemical, and biological phenomena can be expressed in terms of nonlinear partial differential equations. It is difficult to obtain the exact solution for these equations. Analytical methods have been used to find approximate solutions. Many analytical methods such as the Adomian decomposition method [1] [2], the homotopy analysis method [3] [4], the variational iteration method [5] [6], the homotopy perturbation method [7]-[10], and variational homotopy perturbation method [11] [12] have been utilized to solve linear and nonlinear equations. We will use variational homotopy perturbation method to study the Modified Camassa-Holm and Degasperis-Procesi equations and obtain their analytical solutions. (2015) A New Analytical Study of Modified CamassaHolm and Degasperis-Procesi Equations.
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