A new type of multiple-lump and interaction solution of the Kadomtsev-Petviashvili I equation

In this paper, the solution in the form of Grammian of the Kadomtsev-Petviashvili I equation is employed to investigate a new type of multiple-lump solution. The bound state called lump molecules appears in a period of time. A generalized form of the N-lump solutions in N-order determinant possessing the structure of lump molecules is explicitly given. Utilizing the nonzero constant matrices and a non-homogeneous polynomial, the interaction solutions between the multiple-lump waves and the line solitons are constructed. The interactions among the N-lumps and between lumps and solitons are investigated with the aid of numerical simulation. The results extend the understanding of the multiple lumps and interaction dynamical behaviors of the Kadomtsev-Petviashvili I equation.

Automated summary

In this paper, the Grammian solution of the Kadomtsev-Petviashvili I equation is used to investigate a new type of multiple-lump solution. The interaction solutions between multiple-lump waves and line solitons are constructed using nonzero constant matrices and a non-homogeneous polynomial. Numerical simulations are used to investigate the interactions among the multiple lumps and between lumps and solitons, extending the understanding of the dynamics of the Kadomtsev-Petviashvili I equation.