Nonlinearization of the 3 * 3 Matrix Eigenvalue Problem Related to Coupled Nonlinear Schrodinger Equations

摘要

The nonlinearization method is extended to the investigation of coupled nonlinear Schrodinger equations associated with a 3 * 3 matrix eigenvalue problem, from which a new finite-dimensional Hamiltonian system is obatined by nonlinearization of the eigenvalue problem and its adjoint one. A scheme for generating involutive systems of conserved integrals is proposed, by which the finite-dimensional Hamiltonian system is further proved to be completely integrable in the Liouville sense.