Variational Homotopy Perturbation Method for the Nonlinear Generalized Regularized Long Wave Equation

Abstract

This paper presents Variational Homotopy Perturbation method for the nonlinear GeneralizedRegularized Long Wave (GRLW) equation. The solution of nonlinear GRLW equation is obtained and is solved using the iteration method which is combination of Variational Iteration method and Homotopy Perturbation Method. An example of the propagation of single soliton is given to show the precision of this method.

Variational Homotopy Perturbation Method for Solving Riccati Type Differential Problems

“…As we see, the procedure is formulated by the coupling of VIM and HPM [11] [12] [13]. A comparison of like powers of p give solutions of various orders.…”

Solitons and Periodic Solutions of the Fisher Equation with Nonlinear Ordinary Differential Equation as Auxiliary Equation

“…For the past few decades, a vast research has been going on to construct explicit solutions of NLEEs, which are used as models in order to describe many important and problematics physical phenomena in various fields of science. So to figure out the exact solutions of NLEEs substantial work are being made by mathematicians and scientists and have developed effective and convincing methods such as the Hirota's bilinear transformation method [1], the tanh-function method [2,3], the exp-function method [4,5], the F-expansion method [6], the Jacobi elliptic function method [7], the homogeneous balance method [8], the homotopy perturbation method [9], the tanh-coth method [10], the direct algebraic method [11], the Backlund transformation method [12], and others [13,14,15,16].…”