https://doi.org/10.1140/epjp/s13360-023-03924-3
Regular Article
New type of multiple lumps, rogue waves and interaction solutions of the Kadomtsev-Petviashvili I equation
1
College of mathematics, Taiyuan University of Technology, 030024, Taiyuan, Shanxi, PR China
2
School of Mathematics, North University of China, 030051, Taiyuan, Shanxi, PR China
Received:
19
January
2023
Accepted:
22
March
2023
Published online:
3
April
2023
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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.