Optical solitons for Biswas–Arshed equation with multiplicative noise via Itô calculus using three integration algorithms

Zayed, Elsayed M.E.; Shohib, Reham M.A.; Gepreel, Khaled A.; Nofal, Taher A.; Yıldırım, Yakup

doi:10.1016/j.ijleo.2022.168847

Cited by 17 publications

(7 citation statements)

References 34 publications

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“…Previous studies have employed stochastic nonlinear Schrödinger equations to describe the behavior of stochastic optical solitons in nonlinear media. These equations have been extensively discussed in literature, with references such as [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

Shehab,

El‐Sheikh,

Ahmed

et al. 2023

Math Methods in App Sciences

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The improved modified extended tanh‐function approach was used to study optical stochastic soliton solutions and other exact stochastic solutions for the nonlinear Schrödinger‐Hirota equation with multiplicative white noise. The derived solutions include stochastic bright solitons, stochastic singular solitons, stochastic periodic solutions, stochastic singular periodic solutions, stochastic exponential solutions, stochastic rational solutions, and stochastic Jacobi elliptic doubly periodic solutions. Constraints on the parameters were taken into account to ensure the existence of the obtained stochastic soliton solutions. Additionally, selected solutions were presented graphically to illustrate the physical characteristics of the stochastic solutions. In this paper, we used Mathematica (11.3) packages to find the coefficients and Matlab (R2015a) packages to plot the graphs.

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Section: Introductionmentioning

confidence: 99%

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

Shehab,

El‐Sheikh,

Ahmed

et al. 2023

Math Methods in App Sciences

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“…In the past, a number of approaches have been investigated for such governing models [18][19][20][21][22][23]. Dark, bright and singular soliton solutions of the stochastic equations were obtained by Zayed et al using the unified Riccati equation approach [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Exact solutions and dynamic properties of the stochastic governing model for embedded solitons with χ2 and χ3 nonlinear susceptibilities

Chen

2023

Preprint

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This paper studies the exact solutions and dynamic properties of the stochastic governing model for embedded solitons with χ 2 and χ 3 nonlinear susceptibilities. We propose a new trial equation method to find the exact solutions of the model. We also analyze the dynamic properties of the model equation by complete discriminant system for polynomial method. In addition, we assign specific values to the parameters to prove the existence of exact solutions, and giving the two-dimensional diagrams to demonstrate the dynamical behavior of the model. The obtained abundant exact solutions are beneficial for better study of the stochastic perturbation model of optical solitons.

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“…Recently, many experts and scholars have applied some well-known methods to construct analytical solutions of SPDE. ese methods mainly include the sinecosine method [6], the extended (G′/G)-expansion method [7,8], the generalized (G ′ /G)-expansion method [9,10], the Jacobi-elliptic equation scheme [11], and so on [12].…”

Section: Introductionmentioning

confidence: 99%

“…e stochastic nonlinear Biswas-Arshed equation in the Itô calculus sense is a very important class of SPDE. e main purpose of this paper is to analyze the dynamic behavior and exact traveling wave solutions of the stochastic nonlinear Biswas-Arshed equation in the Itô calculus sense as follows (see [11]):…”

Section: Introductionmentioning

confidence: 99%

“…e constant coefficients a 1 , a 2 , σ, b 1 , b 2 , λ, μ, and θ represent different meanings in the nonlinear optics. (1) was first proposed by Elsayed et al In [11], the optical soliton solution of (1) is discussed by using the unified Riccati equation method, the extended auxiliary equation method, and the Jacobi-elliptic equation method, respectively. Especially, when σ � 0, (1) becomes the well-known Biswas-Arshed equation.…”

Section: Introductionmentioning

confidence: 99%

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Phase Portraits and Bounded and Singular Traveling Wave Solution of Stochastic Nonlinear Biswas–Arshed Equation

Tang

Zeng

2022

Discrete Dynamics in Nature and Society

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The main purpose of the current paper is to study the phase portraits and bounded and singular traveling wave solution of the stochastic nonlinear Biswas–Arshed equation by using the “three-step method” of Professor Li’s method together with the phase orbit of planar dynamical system. Firstly, by employing the traveling wave transformation, the stochastic nonlinear Biswas–Arshed equation is simplified into deterministic nonlinear ordinary differential equation. Secondly, phase portraits of the stochastic nonlinear Biswas–Arshed equation are plotted by analyzing the planar dynamic system of the nonlinear ordinary differential equation. Finally, the bounded and singular traveling wave solutions of the stochastic nonlinear Biswas–Arshed equation are constructed.

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Optical solitons for Biswas–Arshed equation with multiplicative noise via Itô calculus using three integration algorithms

Cited by 17 publications

References 34 publications

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

Exact solutions and dynamic properties of the stochastic governing model for embedded solitons with χ2 and χ3 nonlinear susceptibilities

Phase Portraits and Bounded and Singular Traveling Wave Solution of Stochastic Nonlinear Biswas–Arshed Equation

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