Breather wave solutions for the Kadomtsev‐Petviashvili equation with variable coefficients in a fluid based on the variable‐coefficient three‐wave approach

Abstract

Herein, the Kadomtsev‐Petviashvili equation with variable coefficients is investigated, which describes the long waves with small amplitude and slow dependence on the transverse coordinate in a single‐layer shallow fluid. Breather wave solutions are obtained based on a variable‐coefficient three‐wave approach. The dynamical behaviors of the obtained solutions are graphically discussed for different choices of the free parameters in these solutions.