https://doi.org/10.1140/epjp/s13360-020-00371-2
Regular Article
Stochastic treatment of the solutions for the resonant nonlinear Schrödinger equation with spatio-temporal dispersions and inter-modal using beta distribution
1
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
2
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
3
Department of Mathematics, Faculty of Science, Firat University, 23119, Elazig, Turkey
4
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
* e-mail: minc@firat.edu.tr
Received:
9
January
2020
Accepted:
30
March
2020
Published online:
22
April
2020
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 Schrödinger 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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020