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High-order breathers, lumps and hybrid solutions to the (2+1)-dimensional fifth-order KdV equation

Wen-Tao Li

School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P. R. China

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Zhao Zhang

School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P. R. China

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Xiang-Yu Yang

School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P. R. China

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, and

Biao Li

School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P. R. China

E-mail Address: libiao@nbu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0217979219502552Cited by:16 (Source: Crossref)

Abstract

In this paper, the (2+1)-dimensional fifth-order KdV equation is analytically investigated. By using Hirota’s bilinear method combined with perturbation expansion, the high-order breather solutions of the fifth-order KdV equation are generated. Then, the high-order lump solutions are also derived from the soliton solutions by a long-wave limit method and some suitable parameter constraints. Furthermore, we extend this method to obtain hybrid solutions by taking long-wave limit for partial soliton solutions. Finally, the dynamic behavior of these solutions is presented in the figures.

Keywords:

PACS: 05.45.Yv, 02.30.Ik, 52.35.Mw

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