A Finite-Dimensional Integrable System Related to the Complex 3 × 3 Spectral Problem and the Coupled Nonlinear Schrödinger Equation

Lanxin Chen, Junxian Zhang

Shijiazhuang University, Shijiazhuang 050035, China.

DOI: 10.4236/wjet.2015.33C048                

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 Schr?dinger 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. Furthermore, the representation of the solution to the evolution equations is generated by the commutable flows of the finite-dimensional completely integrable system.

Keywords

Integrable System, Evolution Equation, Spectral Problem, Commutable Flows

Conflicts of Interest

The authors declare no conflicts of interest.

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