Investigation of new solitary stochastic structures to the Heisenberg ferromagnetic spin chain model via a Stratonovich sense - Md. Nur Alam (Partial Differential Equations in Applied Mathematics)
This study examines how Stratonovich integrals (SIs) affect the solutions of the Heisenberg ferromagnetic spin chain (HFSC) equation using the modified (G'/G)-expansion (MG'/GE) scheme. By using arbitrary parameters, it formulates traveling wave solutions in rational, trigonometric, and hyperbolic forms. These solutions are vital for elucidating complex phenomena in plasma physics, optical fibers, quantum mechanics, superfluids, and other fields. The research employs both Itô and Stratonovich stochastic calculus (SSC) to assess the dynamic behavior of these random solutions, providing graphical representations to effectively demonstrate these behaviors. The results offer significant insights into understanding and modeling intricate behaviors across various scientific and engineering fields, showcasing the versatility and applicability of the MG'/GE scheme for addressing complex nonlinear evolution equations (NLEEs) influenced by stochastic processes. The dynamic properties and features of these solutions are extensively examined through 3-dimensional, 2-dimensional and contour plots. These graphical representations illustrate a variety of forms, such as periodic solitons, multiple solitons, singular solitons, bright-dark solitons and solitary waves. Furthermore, we relate our mathematical findings to real-world phenomena, enhancing the depth and significance of our research. This analysis centers on how phase shifts depend on various parameters and compares these shifts with those found in exact soliton solutions. With the help of Maple, a robust computer algebra system, we generate generalized solitons and examine their dynamic behavior by exploring parameter values and their interrelations. Solitons, as localized wave phenomena, play a significant role in many areas of nonlinear science, such as quantum mechanics, plasma physics, fluid dynamics, water engineering, and optical fiber technology.