Solitary Waves for the Modified Korteweg-De Vries Equation in Deterministic Case and Random CaseAbdelrahman MAE*
Department of Mathematics, Faculty of Science, Mansoura University, Egypt
- *Corresponding Author:
- Abdelrahman MAE
Department of Mathematics, Faculty of Science
Mansoura University, Egypt
E-mail: [email protected]
Received Date: January 25, 2017; Accepted Date: February 27, 2017; Published Date: March 03, 2017
Citation: Abdelrahman MAE (2017) Solitary Waves for the Modified Korteweg-De Vries Equation in Deterministic Case and Random Case. J Phys Math 8: 214. doi: 10.4172/2090-0902.1000214
Copyright: © 2017 Abdelrahman MAE. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
In this paper, we present a new method, the so called Riccati-Bernoulli Sub-ODE method to construct exact traveling wave solutions of the nonlinear modified Korteweg-de Vries (mKdV) equation and also,we use this method in order to solve the nonlinear random modified Korteweg-de Vries (mKdV) equation. It has been shown that the proposed method is effective tools to in order to solve many mathematical physics problems. The travelling wave solutions of these equations are expressed by hyperbolic functions, trigonometric functions and rational functions. The impression of the random coefficient in our problem is studied, by using some distributions through some cases studies.