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Study of lump solutions to dimensionally reduced generalized KP equations

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Abstract

In this paper, a new (\(3+1\))-dimensional generalized KP (gKP) equation is presented, and two classes of lump solutions, rationally localized in all directions in the space, to the dimensionally reduced cases in (\(2\,+\,1\))-dimensions are derived as well. The proposed method in this work is based on a Hirota bilinear differential equation, which implies that we can build the lump solutions to the presented reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Moreover, there are totally six free parameters in the resulting lump solutions, so that we can get the sufficient and necessary conditions guaranteeing analyticity and rational localization of the solutions by using these six free parameters. In the meantime, two special cases are plotted as illustrative examples and some contour plots with different determinant values are given to show that the corresponding lump solution tends to zero when the determinant approaches zero.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 11101029, 11271362 and 11375030), the Fundamental Research Funds for the Central Universities (No. 610806), Beijing City Board of Education Science and Technology Key Project (No. KZ201511232034), Beijing Nova program (No. Z131109 000413029), and Beijing Finance Funds of Natural Science Program for Excellent Talents (No. 2014000026833ZK19).

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  1. Department of Applied Mathematics, University of Science and Technology Beijing, Beijing, 100083, China

    Jian-Ping Yu

  2. Department of Mathematics, Beijing University of Chemical Technology, Beijing, 100029, China

    Yong-Li Sun

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Yu, JP., Sun, YL. Study of lump solutions to dimensionally reduced generalized KP equations. Nonlinear Dyn 87, 2755–2763 (2017). https://doi.org/10.1007/s11071-016-3225-z

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