Resonant multiple wave solutions to a new (3+1)-dimensional generalized Kadomtsev–Petviashvili equation: Linear superposition principle

Abstract

Linear superposition principle is applied to the Hirota bilinear form of a new (3+1)-dimensional generalized Kadomtsev–Petviashvili equation, which leads to a sufficient and necessary criterion for the existence of linear subspaces of exponential traveling wave solutions. As a result, resonant multiple wave solutions are derived and plotted for the new (3+1)-dimensional generalized Kadomtsev–Petviashvili equation.