The Decomposition And The Quasi-periodic Solutions Of The Nls-mkdv Hierarchy

Based on a 3×3 eigenvalue problem, the hierarchy of NLS-MKdV is presented. With the help of the nonlinearization approach of eigenvalue problems, a new finite-dimensional Hamiltonian system with a Lie-Poisson structure on the Poisson manifold R^3N is obtained. The Abel-Jacobi coordinates are introduced suitably to straighten out the Hamiltonian flows. Based on the decomposition and the theory of algebra curve, the explicit quasi-periodic solutions for the hierarchy are obtained.