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Theoretical study demonstrates stable analytical soliton solutions in nonlinear wave models, indicating robust physical propagation across optics and plasma systems.
The Aigerim-Ratbay-Shyngys equation is used to model ultrashort optical soliton propagation in nonlinear media, Alfvén soliton waves in magnetized plasmas, soliton dynamics in anharmonic lattices, and traffic soliton phenomena. The Akbota-Bayan-Myrzakulov equation describes nonlinear spin dynamics, geometric motion of curves and surfaces, and optical soliton propagation in telecommunications. In this article, we have investigated the fresh and broad spectral soliton solutions for the above models and their corresponding wave profiles as well by using the enhanced modified simple equation method. It is illustrated that the waveform features play an important role in the change of the associated free parameters. The soliton solutions are obtained by equating the exponents of the highest-order linear and nonlinear terms in the governing models. As a result, a variety of exact solutions for both models are obtained, including dark solitons, bright solitons, and singular profiles. The Lyapunov stability analysis demonstrates that both systems are dynamically stable. The solutions obtained in this study are further general and widely applicable and contain some unique forms that have not been reported in previous studies.
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Datta et al. (2026) studied this question.
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