Darboux transformation and Crum's formula for multi-component integrable equations

We present the Darboux transformation and the N-soliton solution for the mu lti-component integrable equations which are associated with the Hermitian symmetric spaces. Using the Darboux covariance, we derive new integrable eq uations as well as known ones including the multi-component extensions of t he nonlinear Schrodinger, the modified KdV, the SIT and the sine-Gordon equ ations. 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 tran sformation is explained. (C) 2001 Elsevier Science BN. All rights reserved.