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The Third Kind Of Darboux Transformation And Multisoliton Solutions For Generalized Broer-Kaup Equations, Sheng Zhang, Dong-Dong Liu

Turkish Journal of Physics

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$N$.