World Journal of Engineering and Technology

Volume 3, Issue 3 (October 2015)

ISSN Print: 2331-4222   ISSN Online: 2331-4249

Google-based Impact Factor: 1.03  Citations  

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    2,899 Downloads   3,539 Views  Citations

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.

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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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