Bilinear auto-Bäcklund transformation, shock waves, breathers and X-type solitons for a (3 + 1)-dimensional generalized B-typeKadomtsev-Petviashvili equation in a fluid

Lu Zheng; Bo Tian; an-Yu Yang; ian-Yu zhou

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Bilinear auto-Bäcklund transformation, shock waves, breathers and X-type solitons for a (3 + 1)-dimensional generalized B-typeKadomtsev-Petviashvili equation in a fluid

Lu Zheng 1, Bo Tian 2 *,an-Yu Yang 3,ian-Yu zhou 3

1. College of Science, Beijing University of Posts and Telecommunications, Beijing 100876

2.College of Science, Beijing University of Posts and Telecommunications, Beijing 100876

3. College of Science, Beijing University of Posts and Telecommunications, Beijing 100876

*Correspondence author

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Funding: National Natural Science Foundation of China （No.11772017）, National Natural Science Foundation of China （No.11272023）, National Natural Science Foundation of China （No.11471050）, State Key Laboratoryof Information Photonics and Optical Communications （No.2017ZZ05）, Fundamental Research Funds forthe Central Universities of China （No.2011BUPTYB02）

Opened online:24 March 2023

Accepted by: none

Citation: Lu Zheng, Bo Tian,an-Yu Yang.Bilinear auto-Bäcklund transformation, shock waves, breathers and X-type solitons for a (3 + 1)-dimensional generalized B-typeKadomtsev-Petviashvili equation in a fluid[OL]. [24 March 2023] http://en.paper.edu.cn/en_releasepaper/content/4759652

In this paper, a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in a fluid, which is used to describe the long waves and has the application in water percolation, is investigated. Via the Hirota method, a bilinear auto-Bäcklund transformation as well as shock-wave, breather and X-type soliton solutions are obtained. The shock waves and breathers are showed. The amplitudes and shapes of shock waves and breathers keep unchanged during the propagation. The X-type soliton on a periodic background are observed. The influence of the coefficients in the equation on the above waves are analysed.

Keywords:Fluid; (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation; Bilinear auto-Bäcklund transformation; Shock waves; Breathers; X-type solitons

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