Abstract
Abstract
Numerous methodologies employed for the exploration of soliton solutions within nonlinear models demonstrate considerable efficacy and efficiency in addressing individual nonlinear partial differential equations (NLPDEs). However, their efficacy diminishes when applied to interconnected NLPDEs, owing to the presence of interaction terms in the coupled equations. Consequently, deriving exact solutions for such coupled equations presents a formidable challenge. In response to this challenge, several researchers have endeavored to solve coupled equations by assuming a proportional relationship between the solution in one line and that in another line, resulting in the imposition of excessive constraints and the subsequent reduction of coupled equations to a single equation. Regrettably, this approach compromises the fidelity of the physical phenomena that these equations aim to describe. In contrast, we propose a method characterized by its simplicity and directness, providing a more authentic and insightful analytical perspective for the investigation of coupled NLPDEs. The innovation lies in its capability to simultaneously propagate different types of solitons in two lines with a single operation, while also enabling the natural emergence of analogous solitons in both systems under minimal constraints. We apply this method to scrutinize the propagation of a diverse range of novel coupled progressive solitons in magneto-optical waveguides featuring a parabolic-nonlocal law of nonlinearity and governed by coupled nonlinear Schrödinger equations. The resultant solitons, depicted through detailed 2D and 3D visualizations in figures 1–12 demonstrate a multitude of coupled soliton forms, several of which are novel in the field.