We present the Darboux transformation and the N-soliton solution for the multi-component integrable equations which are associated with the Hermitian symmetric spaces. Using the Darboux covariance, we derive new integrable equations as well as known ones including the multi-component extensions of the nonlinear Schrödinger, the modified KdV, the SIT and the sine-Gordon equations. We also derive a closed form of the N-soliton solution in terms of the generalized Crum's formula. The projection property of the Darboux transformation is explained.
Bibliographical noteFunding Information:
This work was supported in part by the Brain Korea 21 Project and by the Institute of Information Technology Assessment. Q.-H.P. is also supported in part by KOSEF-2000-1-11200-003-1 and KRF-2000-015-DP0168.
- Crum's formula
- Darboux transformation
- N-soliton solution
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics