The Analytical Solutions of the Stochastic mKdV Equation via the Mapping Method

Abstract

Here, we analyze the (2+1)-dimensional stochastic modified Kordeweg–de Vries (SmKdV) equation perturbed by multiplicative white noise in the Stratonovich sense. We apply the mapping method to obtain new trigonometric, elliptic, and rational stochastic fractional solutions. Because of the importance of the KdV equation in characterizing the behavior of waves in shallow water, the obtained solutions are beneficial in interpreting certain fascinating physical phenomena. We plot our figures in MATLAB and show several 3D and 2D graphical representations to show how the multiplicative white noise affects the solutions of the SmKdV. We show that the white noise around zero stabilizes SmKdV solutions.

Abundant optical soliton solutions for the stochastic fractional fokas system using bifurcation analysis

“…Solving SPDEs is a challenging task due to the interplay between randomness and spatial-temporal dynamics. In recent years, the exact solutions for some SPDEs, for example coupled Korteweg-De Vries [3], mKdV equation [4], Davey-Stewartson equation [5], (4 + 1)-dimensional Fokas equation [6] and etc, have been acquired.…”

Renormalization Group Method for a Stochastic Differential Equation with Multiplicative Fractional White Noise

“…In view of the above special properties, stochastic differential equations driven by fractional Brownian motion have been used as models for many practical problems [6][7][8][9], and the theory has been further developed [10]. The research on infinite-dimensional stochastic differential equations driven by fractional white noise, especially multiplicative noise, has also developed.…”

The Solitary Solutions for the Stochastic Jimbo–Miwa Equation Perturbed by White Noise

“…The use of stochastic NEEs for developing mathematical models of complex processes is on the rise in many fields, including materials sciences, condensed matter climate, finance, information systems, electrical engineering, biophysics and physics system modeling [14,15]. In recent years, analytical solutions for some stochastic NEEs have been acquired, for example [16][17][18][19][20] and the references therein.…”