| 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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