Constructing Traveling Wave Solutions via a Generalized Expansion Method for Nonlinear Evolution Equations Possessing Variable Coefficients

In this article, a highly generalized way of studying nonlinear evolution equations (NLEEs) with time‐dependent variable coefficients is provided. The innovative exact solutions of the Kadomtsev–Petviashvili (KP) equation and the modified Korteweg–de Vries (mKdV) equation with temporal variable coefficients are evaluated by using the extended generalized ‐expansion method. Ion–acoustic waves, ferromagnets, and traffic flow models are all described by the mKdV equation, while shallow‐water waves, plasma physics, and nonlinear optics in two dimensions are explained by the KP equation. The governing equations must incorporate variable coefficients that account for the nonuniform properties of the medium in space and time. The obtained exact solutions of NLEEs are in both hyperbolic and trigonometric forms. The achieved closed‐form solutions are illustrated in the form of 3‐D and contour plots with the aid of Mathematica‐13.3. Dynamical structures, solitary waves, and periodic solitary waves resemble these results.