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

Q. Han Park; H. J. Shin

doi:10.1016/S0167-2789(01)00292-5

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

Q. Han Park, H. J. Shin

Research output: Contribution to journal › Article › peer-review

46 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 language	English
Pages (from-to)	1-15
Number of pages	15
Journal	Physica D: Nonlinear Phenomena
Volume	157
Issue number	1-2
DOIs	https://doi.org/10.1016/S0167-2789(01)00292-5
Publication status	Published - 2001 Sept 1
Externally published	Yes

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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10.1016/S0167-2789(01)00292-5

Cite this

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title = "Darboux transformation and Crum's formula for multi-component integrable equations",

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 Schr{\"o}dinger, 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.",

keywords = "Crum's formula, Darboux transformation, N-soliton solution",

author = "Park, {Q. Han} and Shin, {H. J.}",

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.",

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AU - Park, Q. Han

AU - Shin, H. J.

N1 - 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.

PY - 2001/9/1

Y1 - 2001/9/1

N2 - 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.

AB - 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.

KW - Crum's formula

KW - Darboux transformation

KW - N-soliton solution

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

Abstract

Keywords

ASJC Scopus subject areas

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