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On the role of \(K+L+M\)-wave mixing effect in the (2+1)-dimensional KP I equation

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Abstract

The effect of \(K+L+M\)-wave mixing in the (2+1)-dimensional Kadomtsev–Petviashvili I (KP I) equation is investigated. We give a general auxiliary function to obtain the interaction solutions of KP I equation by the Hirota bilinear method and the long wave limit approach. If we choose different values of K, L, M in the general auxiliary function, we will obtain different types interaction solutions, including superposition of Kth-order lump, L-breather and M-soliton solutions. By strengthening the \(K+L+M\)-wave mixing parameters, the relation of the parameters is given and the interaction solutions are classified via the formula of the general auxiliary function.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under (Grant Nos. 11861050, 11261037), the Natural Science Foundation of Inner Mongolia Autonomous Region, China under (Grant No. 2020LH01010) and Inner Mongolia Normal University graduate students’ research and Innovation fund (Grant No. CXJJS19099).

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Authors and Affiliations

  1. College of Mathematics Science, Inner Mongolia Normal University, Hohhot, 010022, People’s Republic of China

    Dan Zhao &  Zhaqilao

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  1. Dan Zhao
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  2. Zhaqilao
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Correspondence to Zhaqilao.

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Zhao, D., Zhaqilao On the role of \(K+L+M\)-wave mixing effect in the (2+1)-dimensional KP I equation. Eur. Phys. J. Plus 136, 399 (2021). https://doi.org/10.1140/epjp/s13360-021-01372-5

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