New type of multiple lumps, rogue waves and interaction solutions of the Kadomtsev-Petviashvili I equation

In this paper, the theory of four operators is employed to construct the solutions of the KPI equation in form of Grammian. The 1-lump, 3-lump, 6-lump and high-order lump wave solutions are constructed by means of a non-homogeneous polynomial. All the lumps will experience a anomalous scattering with the change of time. The high-order rogue wave solutions describing the multiple-lump molecule exchanging among the resonant solitons are obtained, which can be regarded as a new nonlinear phenomenon of multiple molecular states. Furthermore, the unified scheme for constructing the interaction solutions of N-resonant solitons radiating N-lump molecule is proposed. The characteristics of the anomalous interactions among the lumps and between the lumps and resonant solitons have been investigated in detail. All the obtained solutions are illustrated graphically and useful in describing the nonlinear physical processes in many fields including nonlinear optics, atmosphere, Bose-Einstein condensate and ocean waves. The analytical method presented can be further extended to other nonlinear integrable systems in physics to explore complex wave structures.

Automated summary

In this paper, the solutions of the KPI equation are constructed using the theory of four operators and in the form of Grammian. The 1-lump, 3-lump, 6-lump, and high-order lump wave solutions are obtained using a non-homogeneous polynomial. All the lumps undergo anomalous scattering with time. The high-order rogue wave solutions describe the exchange of multiple-lump molecules among resonant solitons, indicating a new nonlinear phenomenon of multiple molecular states. The interaction solutions of N-resonant solitons radiating N-lump molecules are proposed and the anomalous interactions among the lumps and between the lumps and resonant solitons are examined in detail. The obtained solutions are illustrated graphically and have applications in various fields of nonlinear physics.