Existence of Traveling Wave Solutions for the Perturbed Extended Kadomtsev–Petviashvili Equation

ABSTRACT In this paper, we apply geometric singular perturbation theory and Melnikov's method to the ‐dimensional extended Kadomtsev–Petviashvili (eKP) equation with singular perturbations. For the first time, we rigorously establish the existence of solitary wave solutions under KS‐type perturbations, proving that two distinct solitary waves with speeds and persist. These theoretical results are supported by numerical simulations.