The Quasi-Periodic Solutions Of (2+1)-Dimensional Soliton Equations

In this paper,we mainly concern with a new spectral problem and the corresponding finite-dimensional integral systems.First,we obtain the soliton hierarchy from the zero-curvature equation and get Bargmann constaint between potentials and eigenfunctions by the nonlinearization of the eigenvalue problem.In the corresponding symplectic mani-fold,involution and the functional independence of enough conserved integrals are proved.This gives the Liouville integrability of the finite-dimensional Hamiltonian system.Then under the 'window' of Abel-Jacobi coordiates, various flows can be straightened into linear func-tions of the variables of the flows.By the standard Riemann inversion treatment,quasi-periodic solutions in terms of the Riemann-Theta functions of the soliton equations are explicitly constructed.