Noise effect on soliton phenomena in fractional stochastic Kraenkel-Manna-Merle system arising in ferromagnetic materials

Abstract

This work dives into the Conformable Stochastic Kraenkel-Manna-Merle System (CSKMMS), an important mathematical model for exploring phenomena in ferromagnetic materials. A wide spectrum of stochastic soliton solutions that include hyperbolic, trigonometric and rational functions, is generated using a modified version of Extended Direct Algebraic Method (EDAM) namely r+mEDAM. These stochastic soliton solutions have practical relevance for describing magnetic field behaviour in zero-conductivity ferromagnets. By using Maple to generate 2D and 3D graphical representations, the study analyses how stochastic terms and noise impact these soliton solutions. Finally, this study adds to our knowledge of magnetic field behaviour in ferromagnetic materials by shedding light on the effect of noise on soliton processes inside the CSKMMS.

Abundant Closed-Form Soliton Solutions to the Fractional Stochastic Kraenkel–Manna–Merle System with Bifurcation, Chaotic, Sensitivity, and Modulation Instability Analysis

“…It is an adaptable tool for modeling and analyzing a wide range of systems in science, engineering, finance, and other fields because of its multifaceted character and capacity to accurately represents challenging phenomena. So, the fractional stochastic Kraenkel-Manna-Merle system is represented here [24,32]:…”

“…For deeper consideration of nonlinear occurrence and realistic challenges, it is essential to discover closed-form soliton solutions of SFPDEs. According to the quick advancements in nonlinear sciences, a variety of simple and efficient approaches have been developed to obtain closed-form soliton solutions to NLPDEs, including the Hirota method [4,5], the Bernoulli sub-equation method [6,7], the F-expansion method [8], the (G ′ /G 2 )-expansion method [9], the simple equation method [10], the modified auxiliary equation method [11,12], the two variable (G ′ /G, 1/G)-expansion method [13][14][15][16], the Lie symmetric analysis [17], the polynomial complete discriminant system [18], the tanh-coth scheme [19], the Conservation laws method [20], the generalized exponential rational function approach [21,22], the binary bell polynomials method [23], the mapping method [24], the Shehu transform scheme [25], the sine-Gordon expansion [26], the Cole-Hopf transformation method [27,28], the Fan subequation technique [29], the unified method [30], the Khater method [31], the r + mEDAM method [32], the spectral Tau method [33], the G ′ G ′ +G+A -expansion procedure [34][35][36][37][38], the sub-equation method [39], the collocation method [40], the finite element method [41], and the generalized G ′ /G-expansion method …”