TITLE:
A Finite-Dimensional Integrable System Related to the Complex 3 × 3 Spectral Problem and the Coupled Nonlinear Schrödinger Equation
AUTHORS:
Lanxin Chen, Junxian Zhang
KEYWORDS:
Integrable System, Evolution Equation, Spectral Problem, Commutable Flows
JOURNAL NAME:
World Journal of Engineering and Technology,
Vol.3 No.3C,
October
23,
2015
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.