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

摘要

This work deals with the construction of the exact traveling wave solutions for the nonlinear Schrodinger 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.