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Abundant interaction solutions of the KP equation

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Abstract

Based on the Hirota bilinear form of the KP equation, five classes of interaction solutions between lumps and line solitons are generated via Maple symbolic computations. Analyticity is automatically guaranteed for the first four classes of interaction solutions and the last fifth class of interaction solutions with the plus sign and can be easily achieved for the last fifth class of interaction solutions with the minus sign by taking special choices of the involved parameters. The presented interaction solutions reduce to the existing lumps while the hyperbolic function disappears.

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Acknowledgements

The work was supported in part by a university grant XKY2016112 from Xuzhou Institute of Technology, NSFC under the grants 11371326, 11371086 and 1371361, NSF under the grant DMS-1664561, and the Distinguished Professorships by Shanghai University of Electric Power and Shanghai Second Polytechnic University. The authors are also grateful to S. Batwa, X. Gu, S. Manukure, M. McAnally, Y. Zhou X.L. Yong and H.Q. Zhang for their stimulating discussions.

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Yang, JY., Ma, WX. Abundant interaction solutions of the KP equation. Nonlinear Dyn 89, 1539–1544 (2017). https://doi.org/10.1007/s11071-017-3533-y

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  • DOI: https://doi.org/10.1007/s11071-017-3533-y

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