This article is cited in 40 papers

A New $(3+1)$-dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions

Kamyar Hosseini^a, Majid Samavat^b, Mohammad Mirzazadeh^c, Wen-Xiu Ma^defg, Zakia Hammouch<sup>h

a</sup> Department of Mathematics, Rasht Branch, Islamic Azad University, P.O. Box 41335-3516 Rasht, Iran
^b Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914 Guilan, Rasht, Iran
^c Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157 Rudsar-Vajargah, Iran
^d School of Mathematics, South China University of Technology, 510640 Guangzhou, China
^e Department of Mathematics, Zhejiang Normal University, Jinhua, 321004 Zhejiang, China
^f Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
^g Department of Mathematics and Statistics, University of South Florida, FL 33620-5700 Tampa, USA
^h Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam

Abstract: The behavior of specific dispersive waves in a new $(3+1)$-dimensional Hirota bilinear (3D-HB) equation is studied. A Bäcklund transformation and a Hirota bilinear form of the model are first extracted from the truncated Painlevé expansion. Through a series of mathematical analyses, it is then revealed that the new 3D-HB equation possesses a series of rational-type solutions. The interaction of lump-type and 1-soliton solutions is studied and some interesting and useful results are presented.

Keywords: new $(3+1)$-dimensional Hirota bilinear equation, Bäcklund transformation, Hirota bilinear form, rational-type solutions.

MSC: 45K05, 83C15

Received: 07.05.2020
Accepted: 15.06.2020

Language: English

DOI: 10.1134/S156035472004005X

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