Abstract
In this paper, we study multi-soliton solutions and the Cauchy problem for a two-component short pulse system. For the multi-soliton solutions, we first derive an N-fold Darboux transformation from the Lax pair of the two-component short pulse system, which is expressed in terms of the quasideterminant. Then by virtue of the N-fold Darboux transformation we obtain multi-loop and breather soliton solutions. In particular, one-, two-, three-loop soliton, and breather soliton solutions are discussed in detail with interesting dynamical interactions and shown through figures. For the Cauchy problem, we first prove the existence and uniqueness of a solution with an estimate of the analytic lifespan, and then investigate the continuity of the data-to-solution map in the space of an analytic function.
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