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Symmetry Algebra and the Determinant Solutions of the Constrained Discrete Omtsev-Petviashvili Hierarcy

Author: LiMaoHua
Tutor: ChengYi
School: University of Science and Technology of China
Course: Mathematical Physics
Keywords: dKP hierarchy cdKP hierarchy Baker-Akhiezer function Spectral representation Additional symmetries Virasoro algebra Gaugetransformation Wronskian solution
CLC: O175
Type: PhD thesis
Year: 2013
Downloads: 33
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In this paper, symmetry algebra and the analyticity of the discrete KP(dKP) hierarchy are discussed. Firstly, ghost flow of the dKP hierar-chy is defined, then the ghost flow on eigenfunction(adjoint eigenfunction) and spectral representation of Baker-Akhiezer function and adjoint Baker-Akhiezer function are derived. The ghost flow on tau function and another kind of proof of ASvM formula of the discrete KP hierarchy are given. We constructed the additional symmetries of one-component constrained discrete KP (cdKP) hierarchy, and then proved that the symmetry flows formed the Virasoro algebra. The action of the Virasoro symmetry on the tau function of the constrained discrete KP (cdKP) hierarchy is derived. The gauge transfor-mation of the constrained discrete KP hierarchy is constructed explicitly by the suitable choice of the generating functions. Under the m-step successive gauge transformation Tm, we give the transformed (adjoint) eigenfunctions and the τ-function of the transformed Lax operator of the cdKP hierarchy. We also analyzed the Wronskian solution of the eigenfunction of the cdKP hierarchy.

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