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Regular and Chaotic Dynamics, 2020, Volume 25, Issue 4, Pages 383–391
DOI: https://doi.org/10.1134/S156035472004005X (Mi rcd1071) 		 
This article is cited in 35 scientific papers (total in 35 papers)

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

Kamyar Hosseinia, Majid Samavatb, Mohammad Mirzazadehc, Wen-Xiu Madefg, Zakia Hammouchh

a 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
Citations (35)
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DOI: https://doi.org/10.1134/S156035472004005X
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.
Received: 07.05.2020
Accepted: 15.06.2020
Bibliographic databases:
Document Type: Article
MSC: 45K05, 83C15
Language: English
Citation: Kamyar Hosseini, Majid Samavat, Mohammad Mirzazadeh, Wen-Xiu Ma, Zakia Hammouch, “A New $(3+1)$-dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions”, Regul. Chaotic Dyn., 25:4 (2020), 383–391
Citation in format AMSBIB
\Bibitem{HosSamMir20}
\by Kamyar Hosseini, Majid Samavat, Mohammad Mirzazadeh, Wen-Xiu Ma, Zakia Hammouch
\paper A New $(3+1)$-dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 4
\pages 383--391
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\crossref{https://doi.org/10.1134/S156035472004005X}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85088829404}
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    • This publication is cited in the following 35 articles:
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