Exp-function Method for Wick-type Stochastic Combined KdV-mKdV Equations

Exp-function method is proposed to present soliton and periodic wave solutions for variable coefficients combined KdV- mKdV equation. By means of Hermite transform and white noise analysis, we consider the variable coefficients and Wick-type stochastic combined KdV-mKdV equations. As a result, we can construct new and more general formal solutions. These solutions include exact stochastic soliton and periodic wave solutions.Keywords: combined KdV-mKdV equation, Exp-function method, Wick product, Hermite transform, White noise

Generalized Solutions of Wick-type Stochastic KdV-Burgers Equations Using Exp-function Method

Variable coefficients and Wick-type stochastic KdV-Burgers equations are researched. Expfunction method is proposed to present soliton and periodic wave solutions for variable coefficients KdVBurgers equation. Generalized white noise functional solutions for Wick-type stochastic KdV-Burgersequations are showed via Hermite transform and white noise analysis.Keywords: KdV-Burgers equation; Exp-function method; Wick product; Hermite transform; White noise

Rational and multi-wave solutions to nonlinear evolution equations by means of the Exp-function method

In this paper, we present a new application of the Exp-function method to carry out the integration of nonlinear evolution equations in terms of multi-wave and rational solutions. To elucidate the solution procedure, we analytically investigate the Sharma-Tasso-Olver equation and the fifth-order Korteweg de Vries equation. Unlike Hirota's method, our procedure does not require the bilinear formalism of the equations studied

New soliton solutions of the generalized Zakharov equations using He's variational approach

WOS: 000288883800030In this paper, we obtain new soliton solutions of the generalized Zakharov equations by the well-known He's variational approach. The condition for continuation of the new solitary solution is obtained. (C) 2011 Elsevier Ltd. All rights reserved