Investigating stochastic solutions for fourth order dispersive NLSE with quantic nonlinearity

Yazid Alhojilan; Islam Samir; Yazid Alhojilan; Islam Samir

doi:10.3934/math.2023776

AIMS Mathematics

2023, Volume 8, Issue 7: 15201-15213. doi: 10.3934/math.2023776

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Investigating stochastic solutions for fourth order dispersive NLSE with quantic nonlinearity

Yazid Alhojilan ¹,
Islam Samir ^{2
,
,}

1.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
2.
Department of Physics and Mathematics Engineering, Faculty of Engineering, Ain Shams University, Cairo, Egypt

Received: 28 January 2023 Revised: 07 April 2023 Accepted: 16 April 2023 Published: 24 April 2023
MSC : 35C08, 35C09, 35C07

In this paper, the stochastic fourth order nonlinear Schrödinger equation with quantic nonlinearity and affected by multiplicative noise is considered. This model is used to mimic the wave propagation through optical fibers. The improved modified extended tanh method is used to extract optical solutions for the investigated model. Various types of stochastic solutions are provided such as bright soliton, dark soliton, singular soliton, singular periodic solution and Weierstrass elliptic solution. Moreover, Matlab software packages are used to introduce the effect of the multiplicative noise on the raised solutions. The noise intensity is varied to show the robust of the extracted solutions against the noise.
- quantic nonlinearity,
- nonlinear equations,
- partial differential equations,
- stochastic NLSE,
- multiplicative noise
Citation: Yazid Alhojilan, Islam Samir. Investigating stochastic solutions for fourth order dispersive NLSE with quantic nonlinearity[J]. AIMS Mathematics, 2023, 8(7): 15201-15213. doi: 10.3934/math.2023776

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Abstract

In this paper, the stochastic fourth order nonlinear Schrödinger equation with quantic nonlinearity and affected by multiplicative noise is considered. This model is used to mimic the wave propagation through optical fibers. The improved modified extended tanh method is used to extract optical solutions for the investigated model. Various types of stochastic solutions are provided such as bright soliton, dark soliton, singular soliton, singular periodic solution and Weierstrass elliptic solution. Moreover, Matlab software packages are used to introduce the effect of the multiplicative noise on the raised solutions. The noise intensity is varied to show the robust of the extracted solutions against the noise.

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