Four Associated With The Derivative Nonlinear Schrodinger Equation Family (2 +1)-dimensional Soliton Equations Of Quasi-periodic Solutions

(2+l)-dimensional DNLS, mKP, coupled mKP soliton equations are separated into the first two nontrivial (1+1)-dimensional soliton equations in DNLS hierarchy, further into two new compatible Hamiltonian systems of ordinary differential equations. With the help of nonlinearization approach, the Lenard spectral problem related to the DNLS hierarchy is turned into a completely integrable Hamiltonian system with a Lie-Poisson structure on the Poisson manifold C~N x R~N. A generating function approach is introduced to prove the involutivity and the functional independence of the conserved integrals. A clear evolution picture of various flows is given through the window " of Abel-Jacobi coordinates to straighten out the Hamiltonian flows. Based on the decomposition and the theory of algebra curve, the explicit quasi-periodic solutions for the (1+1) and (2+l)-dimensional soliton equations are obtained.