This research implements the homotopy perturbation method to achieve bi-periodic solutions in Korteweg-de Vries equations, suggesting effective computational techniques.
The Korteweg-de Vries equation is a fundamental equation for the study of shallow water waves and plays a crucial role in fluid physics and applied mathematics. The objective of this study is to implement the homotopy perturbation method to solve a class of Korteweg-de Vries equations with bi-periodic numerical solutions. The method is predicated on the selection of appropriate iterative operations, thereby ensuring the numerical solution of the equation is obtained in the form of the trigonometric series.
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Yang et al. (2026) studied this question.
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