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

Q. Han Park, H. J. Shin

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalPhysica D: Nonlinear Phenomena
Volume157
Issue number1-2
DOIs
Publication statusPublished - 2001 Sept 1
Externally publishedYes

Bibliographical note

Funding 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.

Keywords

  • Crum's formula
  • Darboux transformation
  • N-soliton solution

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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