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

2020, Volume 25, Number 4, pp. 383-391

Author(s): Hosseini K., Samavat M., Mirzazadeh M., Ma W., Hammouch Z.

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

Citation: Hosseini K., Samavat M., Mirzazadeh M., Ma W., Hammouch Z., A New $(3+1)$-dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions, Regular and Chaotic Dynamics, 2020, Volume 25, Number 4, pp. 383-391

DOI: 10.1134/S156035472004005X

Access to the full text on the Springer website