Abstract
For exploring the coupled derivative nonlinear Schrodinger (DNLS) equation more systematically, we give the infinitely many conservation laws of it. Then, the modulation instability of the plane wave solutions for the coupled system is discussed. The higher-order semirational solutions, which can be completely classified as three types, for the coupled DNLS equation are constructed by utilizing the particular vector solutions of the Lax pair and the Darboux transformation.
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