Dynamic behaviors of interaction solutions of (3+1)-dimensional Shallow Water wave equation

Abstract

Rational solutions and interaction solutions of the (3+1)-dimensional Shallow Water wave equation are obtained depending on N-soliton solution by the Hirota bilinear method and long wave limit method. And breather, lump solutions and line rogue waves are obtained from two-soliton solution as well as their interaction solutions are derived from four-soliton solution. After the collision, breathers and lumps remain unchanged, but the line rogue wave has a difference. Furthermore, three-soliton solution is discussed, the interactions between some hybrid solutions, such as hybrid solution between the stripe soliton and breather, hybrid solution between stripe soliton and lump solution and so on, are demonstrated in detail. More interestingly, stripe soliton remain unchanged, but the amplitudes of the periodic line waves, lump solutions and rogue waves have a great change after the collision.