Bilinear Bäcklund Transformation, Fission/Fusion and Periodic Waves of a (3+1)-dimensional Kadomtsev-Petviashvili Equation for the Shallow Water Waves

Kadomtsev-Petviashvili (KP)-typed models are used to elucidate certain shallow water waves that arise in plasma physics, marine engineering, ocean physics, fluid dynamics, etc. In this paper, we investigate a (3+1)-dimensional KP equation for the shallow water waves: (1) Via some exchange formulae, a bilinear Backlund transformation and the corresponding soliton-like solutions are constructed. (2) Via symbolic computation, fission/fusion solutions are derived with some parameter conditions in the N-soliton solutions, which are different from those in the existing literature, where N is a positive integer. We graphically display the spatial structures of the fission/fusion waves to supplement the existing literature. (3) Periodic-wave solutions are worked out via the Hirota-Riemann method. Via the asymptotic properties, relation between the periodic-wave and one-soliton solutions is discussed.