Solitary Waves for the Modified Korteweg-De Vries Equation in Deterministic Case and Random Case
| Autor: | Abdelrahman Mae, Sohaly Ma |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
010302 applied physics
Differential equation Mathematical analysis Hyperbolic function Mathematics::Analysis of PDEs Rational function 01 natural sciences 010305 fluids & plasmas symbols.namesake Nonlinear system Nonlinear Sciences::Exactly Solvable and Integrable Systems 0103 physical sciences symbols Trigonometric functions Noether's theorem Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons Random variable Mathematics |
| Zdroj: | Journal of Physical Mathematics. |
| ISSN: | 2090-0902 |
| DOI: | 10.4172/2090-0902.1000214 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|