Eur. Phys. J. Plus (2015) 130: 249
https://doi.org/10.1140/epjp/i2015-15249-3

Regular Article

Solution of the stochastic generalized shallow-water wave equation using RVT technique

¹ Basic Sciences Dept., Higher Tech. Institute, 228, 10th of Ramadan City, Egypt
² Eng. and Applied Sciences Dept., Community College, Um-Elqura Univ., 715, Riyadh, Saudi Arabia
³ Theoretical Research Physics Group, Physics Department, Faculty of Science, Damietta University, 34517, New Damietta City, Egypt

^* e-mail: ahmostafa@uqu.edu.sa

Received: 8 August 2015
Accepted: 9 November 2015
Published online: 14 December 2015

Abstract

In this paper, some exact solutions of the stochastic generalized nonlinear shallow-water wave (SGNSWW) equation are obtained. This equation is an important equation in fluid mechanics field. Opposite to what is usually assumed in the literature, the coefficients of the nonlinear terms in this stochastic nonlinear partial differential equation (SNLPDE) are considered to be random quantities. The random variable transformation (RVT) technique is combined with the modified extended-tanh function method (METFM) to get the stochastic solutions represented by the probability density functions (PDFs) of the solution processes in terms of the PDFs of the random coefficients. These solutions are illustrated graphically along the spacial and time dimensions at a certain wave speed.