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Bäcklund transformation, Lax pair, infinite conservation laws and exact solutions to a generalized ( $2 + 1$ $2 + 1$ )-dimensional equation

School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China

E-mail Address: zhangjinyu0611@163.com

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Mengkun Zhu

https://orcid.org/0000-0002-2214-7025

School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China

E-mail Address: zmk@qlu.edu.cn

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Shuli Liu

School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China

E-mail Address: 17862072579@163.com

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Chunhui Li

School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China

E-mail Address: lch_1008@163.com

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, and

Xiaoli Wang

School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China

E-mail Address: wxlspu@qlu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0217979222501466Cited by:3 (Source: Crossref)

Abstract

In this paper, the integrability of a generalized ( $2 + 1$ $2 + 1$ )-dimensional equation is investigated by using the Bell polynomials and Hirota bilinear method. By appropriate transformation, the bilinear equation is constructed. Some soliton solutions are yielded via the Hirota bilinear method. Then the evolution and collision of the soliton solutions are discussed. Starting from the two-field condition, the bilinear Bäcklund transformation is derived. Linearization of the $𝒴$ -polynomials-typed Bäcklund transformation leads to the Lax pair. Besides, infinite conservation laws are derived by constructing the Riccati-type equation and devergence-type equation.

Keywords:

PACS: 02.30.Ik, 02.30.Jr, 02.60.Cb

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