Quasiperiodic-to-soliton conversions and their mechanisms of the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

Abstract

This paper systematically investigates the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation, which is widely used to describe various nonlinear phenomena in fluid dynamics and plasma physics. The soliton solutions and multi-periodic wave solutions of this equation are constructed using the Hirota bilinear method and the Riemann theta function. The investigation reveals that the one-periodic waves correspond to the renowned one-dimensional surface cnoidal waves, while the two-periodic waves represent a direct extension of the one-periodic waves. Furthermore, the asymptotic properties of the solutions and the transform relationships between quasiperiodic wave solutions and soliton solutions are analyzed. It is discovered that the quasiperiodic wave solutions can degenerate into soliton solutions under a limiting condition.