| ZHOU Zixiang.[J].数学年刊A辑,1999,20(2):195~204 |
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| PARAMETERS OF DARBOUX TRANSFORMATION FOR REDUCED AKNS, KAUP-NEWELL AND PCF SYSTEMS |
| Received:July 02, 1997 Revised:September 09, 1998 |
| DOI： |
| 中文关键词: |
| 英文关键词:Darboux transformation, Spectral parameters,
$u(p,q)$ reduction |
| 基金项目: |
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| 中文摘要: |
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| 英文摘要: |
| For the integrable system with $u(p,q)$ reduction, there is a
well-known sufficient condition to choose the parameters: the
spectral parameters only take two mutually conjugate values and the solutions of the Lax pair should satisfy certain orthogonal
relations. In this paper, the author proves that, for the AKNS system, the Kaup-Newell system and the principal chiral field (PCF), this condition is also necessary for generic potentials with the $u(p,q)$ reduction. For some other reductions, sufficiency and necessity of more constraints are proved. |
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