Application of the Homotopy Perturbation Method to Linear and Nonlinear Schr¨odinger Equations

The new application accelerates the rapid convergence of the series solutions and is used for analytic treatment of these equations.. Some illustrative examples are given to

The traditional perturbation methods are based on assuming a small parameter, and the approximate solutions obtained by those methods, in most cases, are valid only for small values

In this paper, we present an efficient modification of the homotopy perturbation method by using Chebyshev’s polynomials and He’s polynomials to solve some nonlinear

The results show that the method provides a straightforward and powerful mathematical tool for solving various nonlinear integro-differential equations. Key words: He’s

The discretized modified Korteweg- de Vries (mKdV) lattice equation and the discretized nonlinear Schr¨odinger equation are taken as examples to illustrate the validity and the

The approximate and/or exact solutions of the generalized Klein-Gordon- and sine-Gordon-type equations are obtained. We introduce a new type of initial conditions to extend the class

The purpose of the presented paper is to extend the class of solvable Klein-Gordon- and sine-Gordon-type equations by introducing the new type of initial con- ditions.. We apply

64a, 420 – 430 (2009); received September 4, 2008 / revised October 14, 2008 In this work, the homotopy perturbation method proposed by Ji-Huan He [1] is applied to solve both