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In this Letter, we present the third kind of Darboux transformation of the classical Boussinesq system, and discuss its relationship with the two basic Darboux transformations. By applying the Darboux transformations, we obtain the solutions of multiple soliton interactions, including overtaking and head-on collisions.
Two basic Darboux transformations of a spectral problem associated with a classical Boussinesq system are considered in this letter. They are used to generate new solutions of the classical Boussinesq system. An interesting solution of double-peak soliton has been found.
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