The effect of multiplicative noise on the exact solutions of the stochastic Burgers' equation

In this article, the stochastic Hirota–Maccari system forced in the Itô sense by multiplicative noise is considered. We just use the He’s semi-inverse method, sine–cosine method, and Riccati–Bernoulli sub-ODE method to get new stochastic solutions which are hyperbolic, trigonometric, and rational. The major benefit of these three approaches is that they can be used to solve similar models. Furthermore, we plot 3D surfaces of analytical solutions obtained in this article by using MATLAB to illustrate the effect of multiplicative noise on the exact solution of the Hirota–Maccari method.

show abstract

“…where ρ 1 , ρ 2 , ρ 3 are constants. Differentiating equation (33) once with respect to ς, we obtain…”

Section: Riccati-bernoulli Sub-ode Methodsmentioning

confidence: 99%

Exact solutions of Hirota–Maccari system forced by multiplicative noise in the Itô sense

Mohammed

Ahmad

Boulares

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…These soliton molecules form the information transporter across intercontinental distances around the world. Lastly, the nonlinear Schrödinger's equation (NLSE) has been discussed with help of many models [1–32, 33–36]. The aspect of stochastically is one of the features that is less touched, and there are a few papers that have discussed this aspect [3–9].…”

Section: Introductionmentioning

confidence: 99%

Dispersive optical soliton solutions in birefringent fibers with stochastic Kaup–Newell equation having multiplicative white noise

Zayed,

El‐Horbaty,

Gepreel

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

In this article, we study for the first time the stochastic Kaup–Newell equation in birefringent fibers. Three integration algorithms are applied, namely, the unified Riccati equation expansion method, the addendum to Kudryashov's method, and the addendum to modified sub‐ODE method. Many types of optical soliton solutions such as Jacobi‐elliptic function solutions, Weierstrass elliptic function solutions, bright solitons, dark solitons, singular solitons, and periodic function solutions are obtained. Numerical schemes give a visual perspective to the solutions derived analytically.

show abstract

“…Still, it is impossible to find exact results when dealing with linear equations. Many useful methods have been applied to investigate nonlinear fractional partial differential equations, for example, analytical solutions with the help of natural decomposition method of fractional-order heat and wave equations [9], fractional-order partial differential equations with proportional delay [10], fractional-order hyperbolic telegraph equation [11] and fractional-order diffusion equations [12], the variational iterative transform method [13], the homotopy perturbation transform method [14,15], the homotopy analysis transform method [16,17], reduced differential transform method [18,19], qhomotopy analysis transform method [20][21][22][23][24], the finite element technique [25], the finite difference technique [26], and so on [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Novel Investigation of Fractional-Order Cauchy-Reaction Diffusion Equation Involving Caputo-Fabrizio Operator

Alesemi

Iqbal

Abdo

2022

Journal of Function Spaces

View full text Add to dashboard Cite

In this article, the new iterative transform technique and homotopy perturbation transform method are applied to calculate the fractional-order Cauchy-reaction diffusion equation solution. Yang transformation is mixed with the new iteration method and homotopy perturbation method in these methods. The fractional derivative is considered in the sense of Caputo-Fabrizio operator. The convection-diffusion models arise in physical phenomena in which energy, particles, or other physical properties are transferred within a physical process via two processes: diffusion and convection. Four problems are evaluated to demonstrate, show, and verify the present methods’ efficiency. The analytically obtained results by the present method suggest that the method is accurate and simple to implement.

show abstract

The effect of multiplicative noise on the exact solutions of the stochastic Burgers' equation

Cited by 48 publications

References 39 publications

Exact solutions of Hirota–Maccari system forced by multiplicative noise in the Itô sense

Exact solutions of Hirota–Maccari system forced by multiplicative noise in the Itô sense

Dispersive optical soliton solutions in birefringent fibers with stochastic Kaup–Newell equation having multiplicative white noise

Novel Investigation of Fractional-Order Cauchy-Reaction Diffusion Equation Involving Caputo-Fabrizio Operator

Contact Info

Product

Resources

About