A finite-dimensional integrable system related to the complex 3*3 spectral problem and the coupled nonlinear Schrodinger equation

Articles

A finite-dimensional integrable system related to the complex 3*3 spectral problem and the coupled nonlinear Schrodinger equation [CET 2015]
Author(s)
Lanxin Chen
ABSTRACT
The relation between the 3*3 complex spectral problem and the associated completely integrable system is generated. From the spectral problem, we derived the Lax pairs and the evolution equation hierarchy in which the coupled nonlinear Schrodinger equation is included. Then, with the constraints between the potential function and the eigenvalue function, using the nonlineared Lax pairs, a finite-dimensional complex Hamiltonian system is obtained and proved to be completelyintegrable system in the Liouville sense. Furthermore, the representation of the solution to the evolution equations is generated by the commutable flows of the finite-dimensional completely integrable system. integrable system in the Liouville sense. Furthermore, the representation of the solution to the evolution equations is generated by the commutable flows of the finite-dimensional completely integrable system.
KEYWORDS
finite-dimensional integrable system, complex 3*3 spectral problem, coupled nonlinear Schrodinger equation
References