The coupled derivative nonlinear Schr??dinger equation: conservation laws, modulation instability and semirational solutions

摘要： For exploring the coupled derivative nonlinear Schr?dinger (DNLS) equation more systematically, we give the in?nitely 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 classi?ed as three types, for the coupled DNLS equation are constructed by utilizing the particular vector solutions of the Lax pair and the Darboux transformation.