On the stability analysis and the solitonic wave structures for the stochastic resonant nonlinear Schrödinger equation with spatio temporal and inter-modal dispersion under generalized Kudryashov's law non-linearity

Document Type : Research Articles

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1 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.

2 Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar -Vajargah, Iran.

3 Department of Mathematics, University of Okara, Okara, Pakistan.

Abstract

This paper discusses the optical soliton solutions of the stochastic resonant nonlinear Schrödinger equation (SRNLSE). The equation has spatio-temporal dispersion, inter-modal dispersion, multiplicative white noise, and nonlinearity under generalized Kudryashov's law. Optical soliton solutions in terms of bright, dark, periodic, and singular solitons are obtained from this equation by using the (Gˊ)/G^2 -expansion method and a new Kudryashov method. This work provides insight into soliton dynamics in nonlinear optical systems with stochastic effects, where complex dispersion interactions play a dominant role. Specifically, it shows how the interplay of spatio-temporal dispersion (SPD) and inter-modal dispersion (IMD), in the presence of multiplicative noise, determines the behavior of solitons. We also discuss the effects of multiplicative noise on the exact solutions of the nonlinear Schrödinger equation using the Maple software. The stability of critical points is discussed by linearizing the system around equilibrium solutions and graphically indicating the behavior of these solutions as well.

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