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A semidiscrete Boussinesq system has been introduced by the means of recombination flows from a 4×4 spectral problem. We construct the Darboux transformation and explicit solutions for the semidiscrete Boussinesq system. We can find that the 1-fold Darboux-transformation solution of the system possesses more than one traveling waves. Especially, one of solutions comes into being two solitary waves...
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