超对称可积系统和离散可积系统

系统地研究超对称方程解的构造方法，特别是Darboux变换法。讨论在物理中重要的超对称低辰獾募蛄返谋泶锸剑缋伤够辛惺叫问降慕狻Ｑ芯砍猿葡低矰arboux变换的几何涵义。探讨超对称KP的附加对称性在tau函数形式中作用。考虑与离散几何密切相关的离散可积低车男灾省?....

Within the framework of this NNSFC project, we achieved the followings: Darboux transformations are constructed for the supersymmetric KP hierarchies; it is shown that the coupled KdV.of Nutku and Oguz can be decoupled; two Hamiltonian structures for the Ito’s equation are provided; it is proved that the Miura map between the lattice KP and modified lattice KP is canonical.in the sense of the second Hamiltonian structure; a Darboux transformation is given for the modified Veselov-Novikov equation; we also give an explanation of appearance of Pfaffian solutions.for the BKP hierarchy