The third kind of Darboux transformation and multisoliton solutions for generalized Broer–Kaup equations

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 2 N -soliton solutions with parameters of the generalized Broer–Kaup equations are obtained. Although 2 N is an even number, it is graphically shown that in the cases of N = 1 and N = 2 the obtained 2 N -soliton solutions can degenerate into M -soliton solutions for any positive integer M less than 2 N .