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

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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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Rasht Branch, Islamic Azad University, 41335-3516, Rasht, Iran

    Kamyar Hosseini

  2. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, 41335-1914, Rasht, Iran

    Majid Samavat

  3. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, 44891-63157, Rudsar-Vajargah, Iran

    Mohammad Mirzazadeh

  4. Department of Mathematics, Zhejiang Normal University, 321004, Zhejiang, China

    Wen-Xiu Ma

  5. Department of Mathematics, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

    Wen-Xiu Ma

  6. Department of Mathematics and Statistics, University of South Florida, FL 33620-5700, Tampa, USA

    Wen-Xiu Ma

  7. School of Mathematics, South China University of Technology, 510640, Guangzhou, China

    Wen-Xiu Ma

  8. Division of Applied Mathematics, Thu Dau Mot University, 820000, Binh Duong Province, Vietnam

    Zakia Hammouch

Authors
  1. Kamyar Hosseini
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  2. Majid Samavat
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  3. Mohammad Mirzazadeh
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  4. Wen-Xiu Ma
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  5. Zakia Hammouch
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Corresponding authors

Correspondence to Kamyar Hosseini, Majid Samavat, Mohammad Mirzazadeh, Wen-Xiu Ma or Zakia Hammouch.

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MSC2010

45K05, 83C15

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Hosseini, K., Samavat, M., Mirzazadeh, M. et al. A New \((3+1)\)-dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions. Regul. Chaot. Dyn. 25, 383–391 (2020). https://doi.org/10.1134/S156035472004005X

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