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Abstract The paper introduce a novel auxiliary equation method for the successful derivation of traveling wave solutions for the non-linear Kairat-X (K-X) equation. Along with other novel results, soliton, singular, triangular periodic, and doubly periodic topological solutions are among the solutions obtained. The study revisits the concept of optical solitary waves, enhancing our understanding of the model. Previous studies have already derived analytical solutions using diverse approaches, contributing to the discovery of new soliton solutions within this framework. These solutions are characterized through three-dimensional, contour plot, and two-dimensional profile analyses. Additionally, the impact of time on the propagation of wave patterns is explored. The outcomes show how well our suggested approach works to solve non-linear evolution equations by producing fresh, more thorough solutions, making it a powerful mathematical tool for doing so. Through this article, we elucidate how leveraging NAEM with the Kairat-X equation can lead to optimized optical systems, improved data transmission rates, and the evolution of nonlinear optics towards more efficient and reliable communication technologies.
Faridi et al. (Thu,) studied this question.
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