Unveiling New Exact Solutions of the Complex-Coupled Kuralay System Using the Generalized Riccati Equation Mapping Method

Year 2024, Volume: 7 Issue: 3, 146 - 156, 31.12.2024

Bahadır Kopçasız

https://doi.org/10.33187/jmsm.1475211

Abstract

This examination analyzes the integrable dynamics of induced curves by utilizing the complex-coupled Kuralay system (CCKS). The significance of the coupled complex Kuralay equation lies in its role as an essential model that contributes to the understanding of intricate physical and mathematical concepts, making it a valuable tool in scientific research and applications. The soliton solutions originating from the Kuralay equations are believed to encapsulate cutting-edge research in various essential domains such as optical fibers, nonlinear optics, and ferromagnetic materials. Analytical procedures are operated to derive traveling wave solutions for this model, given that the Cauchy problem cannot be resolved using the inverse scattering transform. This study uses the generalized Riccati equation mapping (GREM) method to search for analytical solutions. This method observes single and combined wave solutions in the shock, complex solitary shock, shock singular, and periodic singular forms. Rational solutions also emerged during the derivation. In addition to the analytical results, numerical simulations of the solutions are presented to enhance comprehension of the dynamic features of the solutions generated. The study's conclusions could provide insightful information about how to solve other nonlinear partial differential equations (NLPDEs). The soliton solutions found in this work provide valuable information on the complex nonlinear problem under investigation. These results provide a foundation for further investigation, making the solutions helpful, manageable, and trustworthy for the future development of intricate nonlinear issues. This study's methodology is reliable, robust, effective, and applicable to various NLPDEs. The Maple software application is used to verify the correctness of all obtained solutions.

Keywords

Complex-coupled Kuralay system (CCKS), Soliton solutions, The generalized Riccati equation mapping (GREM) method

Ethical Statement

It is declared that during the preparation process of this study, scientific and ethical principles were followed and all the studies benefited from are stated in the bibliography.

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