Decomposition and straightening out of the coupled mixed nonlinear Schrödinger flows

The nonlinearization approach of Lax pairs is extended to the investigation of a soliton hierarchy proposed by Wadati, Konno and Ichikawa, in which the first nontrivial equation is the coupled mixed nonlinear Schrödinger equation. Under a constraint between the potentials and eigenfunctions, solutions of the soliton hierarchy are decomposed into a class of new finite-dimensional Hamiltonian systems. The generating function of the integrals of motion is presented, by which the class of finite-dimensional Hamiltonian systems are further proved to be completely integrable in the Liouville sense. Based on the decomposition and the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows. As an application, the compatible solutions of the various flows in Abel-Jacobi coordinates are explicitly obtained. © 2003 Elsevier Ltd. All rights reserved.