Abstract
The Broer-Kaup system related to the classical Boussinesq system is discussed by the inverse scattering transform. A symmetry condition with two cases is considered to construct the explicit solutions of the Broer-Kaup system. One case confined the eigenvalues to be pure imaginary implies the kink soliton, another case gives rise to the mixed blowup and breather solutions with kink type background. In the first case, we show a novel inelastic interaction of sector kink solutions.
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