journal article·2024-02-01Open access

A novel motivation for the unstable nonlinear Schrödinger equation through random inputs

Sami M. Albalawi, M. A. Sohaly, M. E. Fares

AIP Advances· Volume 14· Issue 2

Abstract

We investigate the stochastic unstable nonlinear Schrödinger equation through bi-random sources. Specifically, we solve this equation via Itô sense, with the parameter following Laplace and Gumbel distributions. We provide vital stochastic solutions in applied sciences. We employ He’s semi-inverse technique in order to provide these solutions in a unified way. Actually, this is the first time that the same model has been taken into account in these circumstances. In order to investigate the real relevance of the stochastic unstable nonlinear Schrödinger equation, we provide the simulations for some of the collected solutions using the appropriate parameter settings provided by the MATLAB software. Finally, our renewed drive might expand to incorporate further emerging natural science models.
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Research context

OpenAlex topics: Nonlinear Photonic Systems · Quantum chaos and dynamical systems · Fractional Differential Equations Solutions

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

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

References (31)

Show source-provided references
1. Strongly nonlinear stochastic processes in physics and the life sciences10.1155/2013/149169 ↗
2. A stochastic model for internal HIV dynamics10.1016/j.jmaa.2007.11.005 ↗
3. A construction of new traveling wave solutions for the 2D Ginzburg-Landau equation10.1140/epjp/i2019-12811-y ↗
4. Disturbance solutions for the long–short-wave interaction system using bi-random Riccati-Bernoulli sub-ODE method10.1080/16583655.2020.1747242 ↗
5. 1999
6. On the new wave solutions to the MCH equation10.1007/s12648-018-1354-6 ↗
7. On the nonlinear new wave solutions in unstable dispersive environments10.1088/1402-4896/ab62d7 ↗
8. Fundamental solutions to the stochastic perturbed nonlinear Schrödinger’s equation via gamma distribution10.1016/j.rinp.2021.104249 ↗
9. New explicit exact solutions of the unstable nonlinear Schrödinger’s equation using the expa and hyperbolic function methods10.1007/s11082-018-1350-2 ↗
10. 2013
11. 1991
12. 2014
13. Quantifying uncertainty in epidemiological models
14. Strong convergence rate of finite difference approximations for stochastic cubic Schrodinger equations10.1016/j.jde.2017.05.002 ↗
15. Analysis of a splitting scheme for damped stochastic nonlinear Schrodinger equation with multiplicative noise10.1137/17m1154904 ↗
16. Optimal control for stochastic nonlinear Schrodinger equation on graph10.1137/22m1524175 ↗
17. Stochastic logarithmic Schrodinger equations: Energy regularized approach10.1137/21m1442425 ↗
18. Theory of Bose–Einstein condensation in trapped gases10.1103/revmodphys.71.463 ↗
19. Bright and dark optical solitons in fiber media with higher-order effects10.1016/s0960-0779(00)00278-2 ↗
20. Solitary waves for the nonlinear Schrödinger problem with the probability distribution function in the stochastic input case10.1140/epjp/i2017-11607-5 ↗
21. Stochastic treatment of the solutions for the resonant nonlinear Schrödinger equation with spatio-temporal dispersions and inter-modal using beta distribution10.1140/epjp/s13360-020-00371-2 ↗
22. The coupled nonlinear Schrödinger-type equations10.1142/s0217984920500785 ↗
23. Fundamental stochastic solutions for the conformable fractional NLSE with spatiotemporal dispersion via exponential distribution10.1088/1402-4896/ac119c ↗
24. New exact traveling wave solutions of the unstable nonlinear Schrödinger equations10.1088/0253-6102/68/6/761 ↗
25. The propagation of solitary waves in piezoelectric semiconductors10.1088/0022-3719/8/8/022 ↗
26. Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics10.1515/tjj.1997.14.1.23 ↗
27. Variational principles for some nonlinear partial differential equations with variable coefficients10.1016/s0960-0779(03)00265-0 ↗
28. Some asymptotic methods for strongly nonlinear equations10.1142/s0217979206033796 ↗
29. 2002
30. Nonlinear self-modulation of ion-acoustic waves10.1063/1.862198 ↗
31. Modulation instability: The beginning10.1016/j.physd.2008.12.002 ↗