A Super Extension Of The Coupled Harry-Dym Hierarchy

This thesis mainly studies the super extension of the coupled Harry-Dym equation and establishes its super Bi-Hamilton structures and obtains infinite conservation laws.Firstly,based on the zero-curvature equation of the 3 × 3 matrix spectral problem,the hierarchy of super coupled Harry-Dym equation is derived.Then Bi-Hamilton structures of the super coupled Harry-Dym hierarchy are constructed by using the super trace identities.Finally,the infinite conservation laws of the super coupled Harry-Dym equation are obtained with the help of spectral parameter expansion.