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

Chaffee-Infante denklemi için soliton çözümlerinin oluşturulması

In this article, has been studied on the Chaffee-Infante equation and soliton solutions of these equation are examined. In accordance with this purpose, The sine-Gordon expansion method, which is one of the solution methods of nonlinear partial differential equations, was used. Also graphical representation of the obtained results of the specified equation is made using Wolfram Mathematica 12 for certain values and thus the conformity of the founded results has been demonstrated.Bu makalede, Chaffee-Infante denklemi üzerinde çalışılmıştır ve bu denklemin soliton çözümleri incelenmiştir. Bu amaç doğrultusunda, lineer olmayan kısmi diferansiyel denklemlerin çözüm yöntemlerinden biri olan sine-Gordon açılım yöntemi kullanılmıştır. Ayrıca belirtilen denklemin elde edilen sonuçlarının grafiksel gösterimi belli değerler için Wolfram Mathematica 12 programı kullanılarak yapılmış ve böylece bulunan sonuçların uygunluğu gösterilmiştir

Exact traveling wave solutions to the Klein–Gordon equation using the novel (G′/G)-expansion method

AbstractThe novel (G′/G)-expansion method is one of the powerful methods that appeared in recent times for establishing exact traveling wave solutions of nonlinear partial differential equations. Exact traveling wave solutions in terms of hyperbolic, trigonometric and rational functions to the cubic nonlinear Klein–Gordon equation via this method are obtained in this article. The efficiency of this method for finding exact solutions and traveling wave solutions has been demonstrated. It is shown that the novel (G′/G)-expansion method is a simple and valuable mathematical tool for solving nonlinear evolution equations (NLEEs) in applied mathematics, mathematical physics and engineering