The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method

Abstract

This article considers the stochastic fractional Radhakrishnan-Kundu-Lakshmanan equation (SFRKLE), which is a higher order nonlinear Schrödinger equation with cubic nonlinear terms in Kerr law. To find novel elliptic, trigonometric, rational, and stochastic fractional solutions, the Jacobi elliptic function technique is applied. Due to the Radhakrishnan-Kundu-Lakshmanan equation’s importance in modeling the propagation of solitons along an optical fiber, the derived solutions are vital for characterizing a number of key physical processes. Additionally, to show the impact of multiplicative noise on these solutions, we employ MATLAB tools to present some of the collected solutions in 2D and 3D graphs. Finally, we demonstrate that multiplicative noise stabilizes the analytical solutions of SFRKLE at zero.

Exact solutions of the stochastic Maccari system forced by multiplicative noise

“…where 𝜎 is a intensity of noise, 𝑊(𝑡) is the standard Wiener process and 𝑊 𝑡 = 𝜕𝑊 𝜕𝑡 . Three different techniques including sine-cosine, the Riccati-Bernoulli sub-ODE, and He's semi-inverse will be utilized to attain the exact solutions of SMS (3)(4). The results reported here generalize earlier results, such as the finding in [29,32].…”

“…Here, we examine the effects of noise on the acquired solutions of SMS (3)(4). In order to illustrate how these solutions behave, we have various graphical representations.…”

Diverse Variety of Exact Solutions for Nonlinear Gilson–Pickering Equation

“…F = 1 2 pF 4 + qF 2 + r To find out the solutions of Equation ( 10), the JEFM is utilized [65,66]. As a consequence, we are capable of acquiring the solutions of Equation (1).…”

“…Here, the third-order nonlinear GPE [59,60] is solved, and we find possible exact solutions with the help of Sardar's subequation method (SSM) [61][62][63][64], the Jacobi elliptic function method (JEFM) [65,66], and the generalized derivative technique [67]. The GPE can be written as…”

Impact of Multiplicative Noise on the Exact Solutions of the Fractional‐Stochastic Boussinesq‐Burger System

“…Recently, the searching of exact soliton solutions to NLPDEs has become an enthralling research topic in engineering and applied sciences. Many techniques have been used to determine exact solutions for NLPDE including tanh-sech [14,15], Darboux transformation [16], sinecosine [17,18], exp ð−ϕðςÞÞ-expansion [19], ðG ′ /GÞ-expan-sion [20][21][22], Lie symmetry analysis method [23], improved F-expansion method [24,25], Hirota's function [26], the Jacobi elliptic function [27,28], and perturbation [29,30].…”