Stochastic treatment of the solutions for the resonant nonlinear Schrödinger equation with spatio-temporal dispersions and inter-modal using beta distribution

Abstract

In this paper, the extended Jacobian elliptic function expansion method is implemented in order to construct some new traveling wave solutions for the resonant nonlinear Schrodinger equation with both spatio-temporal dispersion and inter-modal dispersion. These new traveling wave solutions are obtained by the proposed method, which is easy to implement and computationally very attractive. Moreover, these solutions may be applicable for some physical fields, such as plasma physics. The main aim of this paper is the stochastic treatment of the solutions when the spatio-temporal coefficient or the wave transition is beta random variables. The priority of using beta statistical distribution for the spatio-temporal is discussed. Some graphical simulations are given to illustrate the behavior of these solutions in the deterministic and stochastic case studies. Indeed the proposed techniques are very powerful tool to solve other models in applied science.