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
2020, vol. 25, no. 4, pp. 383-391
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.