The Integrability Of Restrained NLS System In Complex Spectral Parameters

The thesis is based on the nonlinearized eigenvalue problem of NLS hierarchy. We will focus on a series of conclusions to the nonlinearized eigenvalue problem of NLS hier-archy with complex spectral parameters. At the same time, we contrast the conclusions with those whose spectral parameters are real. From this, we study the Hamilton-Jacobi theory of the generating function with a Lie-Poisson structure. Accordingly, we expand the complex form of the nonlinearized eigenvalue problem of NLS hierarchy.