In this paper, Whitham–Broer–Kaup (WBK) equations with time-dependent coefficients are exactly solved through Hirota’s bilinear method. To be specific, the WBK equations are first reduced into a system of variable-coefficient Ablowitz–Kaup– Newell–Segur (AKNS) equations. With the help of the AKNS equations, bilinear forms of the WBK equations are then given. Based on a special case of the bilin...

In this paper, the space–time fractional Whitham–Broer–Kaup equations are investigated. By means of new scaling transformations, nonlinear system different time and space orders is transformed to integer one. The multiple solitary solutions periodic obtained, respectively. All those given exactly by introducing which makes our study unique from most existing studies. It expected that exact for ...

In this paper, the Painlevé integrable property of (1 + 1)-dimensional generalized Broer–Kaup (gBK) equations is first proven. Then, Bäcklund transformations for gBK are derived by using truncation. Based on a special case transformations, linearized into heat conduction equation. Inspired reduced Burgers Starting from linear equation, two forms N-soliton solutions and rational with singularity...

In this paper, the third kind of Darboux transformation of generalized Broer–Kaup equations is derived from the corresponding spectral problem. By virtue of this Darboux transformation, new 2N -soliton solutions with parameters of the generalized Broer–Kaup equations are obtained. Although 2N is an even number, it is graphically shown that in the cases of N= 1 and N = 2 the obtained 2N -soliton...