Generalized Variational Principle for Long Water-Wave Equation by He's Semi-Inverse Method

Generalized Variational Principle for Long Water-Wave Equation by He's Semi-Inverse Method

Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

Optimization of Solution Regularized Long-wave Equation by Using Modified Variational Iteration Method

In this paper, a regularized long-wave equation (RLWE) is solved by using the Adomian's decomposition method (ADM) , modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by ...

Construction of a solitary wave solution for the generalized Zakharov equation by a variational iteration method

In this paper, the well-known He’s variational iteration method (VIM) is used to construct solitary wave solutions for the generalized Zakharov equation (GZE). The chosen initial solution (trial function) can be in soliton form with some unknown parameters, which can be determined in the solution procedure. c © 2007 Elsevier Ltd. All rights reserved.

Soliton Solutions of the Perturbed Resonant Nonlinear Schrödinger’s Equation with Full Nonlinearity by Semi-Inverse Variational Principle

This paper carries out the integration of the resonant nonlinear Schrödinger’s equation in presence of perturbation terms that are considered with full nonlinearity. The three types of nonlinear media are studied. They are the cubic nonlinearity, power law and log law nonlinearity. The semi-inverse variational principle is applied to extract the analytical soliton solution.