Eur. Phys. J. Plus (2017) 132: 339
https://doi.org/10.1140/epjp/i2017-11607-5

Regular Article

Solitary waves for the nonlinear Schrödinger problem with the probability distribution function in the stochastic input case

Department of Mathematics, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt

^* e-mail: m_stat2000@yahoo.com

Received: 14 May 2017
Accepted: 22 June 2017
Published online: 7 August 2017

Abstract

This work deals with the construction of the exact traveling wave solutions for the nonlinear Schrödinger equation by the new Riccati-Bernoulli Sub-ODE method. Additionally, we apply this method in order to study the random solutions by finding the probability distribution function when the coefficient in our problem is a random variable. The travelling wave solutions of many equations physically or mathematically are expressed by hyperbolic functions, trigonometric functions and rational functions. We discuss our method in the deterministic case and also in a random case, by studying the beta distribution for the random input.