Reductive Perturbation Method and Far Fields of Wave Equations

An Application of Modified Reductive Perturbation Method to Symmetric Regularized-long-wave Equations

In this work, we extended the application of ”the modified reductive perturbation method” to symmetrical regularized long waves with quadratic nonlinearity and obtained various form of KdV equations as the governing equations. Seeking a localized travelling wave solutions to these evolution equations we determined the scale parameters g1 and g2 so as to remove the possible secularities that mig...

Renormalization Group Method and Reductive Perturbation Method

It is shown that the renormalization group method does not necessarily eliminate all secular terms in perturbation series to partial differential equations and a functional subspace of renormalizable secular solutions corresponds to a choice of scales of independent variables in the reductive perturbation method. Recently a novel method based on the perturbative renormalization group theory has...

Numerical method for the wave and nonlinear diffusion equations with the homotopy perturbation method

In this paper, the homotopy perturbation method and a modified homotopy perturbation method are used for analytical treatment of the wave equation and some nonlinear diffusion equations, respectively. Some examples are given to illustrate that a suitable choice of an initial solution can lead to the exact solution, this revealing the reliability and effectiveness of the method. © 2009 Elsevier ...

Reductive Perturbation Method, Multiple–Time Solutions and the KdV Hierarchy

We apply a multiple–time version of the reductive perturbation method to study long waves as governed by the Boussinesq model equation. By requiring the absence of secular producing terms in each order of the perturbative scheme, we show that the solitary–wave of the Boussinesq equation can be written as a solitary–wave satisfying simultaneously all equations of the KdV hierarchy, each one in a...

Far Field Expansion for Anisotropic Wave Equations