Localized waves and interaction solutions to a (3+1)-dimensional generalized KP equation

Abstract

Based on the Hirota bilinear method and long wave limit, four kinds of localized waves, namely, solitons, lumps, breathers, and rogue waves are constructed for the(3+1)-dimensional generalized KP equation. N-soliton solutions are obtained by employing bilinear method, then breathers, two breathers and interaction breather solutions are obtained by selecting appropriate parameters on two-soliton solution and four-soliton solution. These breathers own different dynamic behaviors in the different planes. Taking a long wave limit on the two and four soliton solutions under special parameter constraints, one-order lumps and rogue waves, two-order lumps and rogue waves, and interaction solutions between lumps and rogue waves are derived. Applying the same method on the three soliton solution, interaction solutions between kink solitons with periodic solutions, lumps and rogue waves are constructed, respectively. The influence of parameters on the solution is analyzed. The propagation directions, phase shifts, energies and shapes for these solutions can be affected and controlled by the parameters. Moreover, graphics are presented to demonstrate the properties of the explicit analytical localized wave solutions.