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

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DOI: 10.4236/wjet.2015.33C048    2,479 Downloads   2,738 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Chen, L. and Zhang, J. (2015) A Finite-Dimensional Integrable System Related to the Complex 3 × 3 Spectral Problem and the Coupled Nonlinear Schrödinger Equation. World Journal of Engineering and Technology, 3, 322-327. doi: 10.4236/wjet.2015.33C048.

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