Analytical manner for abundant stochastic wave solutions of extended KdV equation with conformable differential operators

Hyder, Abd‐Allah; Soliman, Ahmed H.

doi:10.1002/mma.7317

Cited by 7 publications

(5 citation statements)

References 56 publications

(107 reference statements)

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“…The noise arising in physics, telecommunication networks, hydrology, medicine, and so on can be modeled by stochastic partial differential equations. One of the important research directions of stochastic partial differential equations is the stochastic wave, which has been studied by many authors (see [1][2][3]). Optical solitons are used to transmit very large amounts of data at the speed of light without error and loss over very long distances (see .…”

Section: Introductionmentioning

confidence: 99%

Stochastic Solitons in Birefringent Fibers for Biswas–Arshed Equation with Multiplicative White Noise via Itô Calculus by Modified Extended Mapping Method

2023

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Stochastic partial differential equations have wide applications in various fields of science and engineering. This paper addresses the optical stochastic solitons and other exact stochastic solutions through birefringent fibers for the Biswas–Arshed equation with multiplicative white noise using the modified extended mapping method. This model contains many kinds of soliton solutions, which are always symmetric or anti-symmetric in space. Stochastic bright soliton solutions, stochastic dark soliton solutions, stochastic combo bright–dark soliton solutions, stochastic combo singular-bright soliton solutions, stochastic singular soliton solutions, stochastic periodic solutions, stochastic rational solutions, stochastic Weierstrass elliptic doubly periodic solutions, and stochastic Jacobi elliptic function solutions are extracted. The constraints on the parameters are considered to guarantee the existence of these stochastic solutions. Furthermore, some of the selected solutions are described graphically to demonstrate the physical nature of the obtained solutions.

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Section: Introductionmentioning

confidence: 99%

Stochastic Solitons in Birefringent Fibers for Biswas–Arshed Equation with Multiplicative White Noise via Itô Calculus by Modified Extended Mapping Method

2023

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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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“…Recently, many authors have found an interest in nonlinear models for stochastic systems of differential equations [26][27][28][29][30], which have numerous applications. They also found both analytical and numerical solutions to their system using various methodologies.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of a Differential System Considering a Pure Hybrid Fuzzy Neutral Delay Theory

et al. 2022

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In this paper, we propose and derive a new system called pure hybrid fuzzy neutral delay differential equations. We apply the classical fourth-order Runge–Kutta method (RK-4) to solve the proposed system of ordinary differential equations. First, we define the RK-4 method for hybrid fuzzy neutral delay differential equations and then establish the efficiency of this method by utilizing it to solve a particular type of fuzzy neutral delay differential equation. We provide a numerical example to verify the theoretical results. In addition, we compare the RK-4 and Euler solutions with the exact solutions. An error analysis is conducted to assess how much deviation from exactness is found in the two numerical methods. We arrive at the same conclusion for our hybrid fuzzy neutral delay differential system since the RK-4 method outperforms the classical Euler method.

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Analytical manner for abundant stochastic wave solutions of extended KdV equation with conformable differential operators

Cited by 7 publications

References 56 publications

Stochastic Solitons in Birefringent Fibers for Biswas–Arshed Equation with Multiplicative White Noise via Itô Calculus by Modified Extended Mapping Method

Stochastic Solitons in Birefringent Fibers for Biswas–Arshed Equation with Multiplicative White Noise via Itô Calculus by Modified Extended Mapping Method

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

Numerical Solutions of a Differential System Considering a Pure Hybrid Fuzzy Neutral Delay Theory

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