Weakly Coupled B-Type Kadomtsev-Petviashvili Equation: Lump and Rational Solutions

Abstract

Through the method of ZN-KP hierarchy, we propose a new (3+1)-dimensional weakly coupled B-KP equation. Based on the bilinear form, we obtain the lump and rational solutions to the dimensionally reduced cases by constructing a symmetric positive semidefinite matrix. Then, we do numerical analysis on the rational solutions and fit the trajectory equation of the crest. Furthermore, we verify the accuracy of the trajectory equation by numerical analysis. This method of solving the lump and rational solutions can also be applied to other nonlinear evolution equations.