|
|
| |
| PARAMETERS OF DARBOUX TRANSFORMATION FOR REDUCED AKNS, KAUP-NEWELL AND PCF SYSTEMS |
| |
Citation： |
ZHOU Zixiang.PARAMETERS OF DARBOUX TRANSFORMATION FOR REDUCED AKNS, KAUP-NEWELL AND PCF SYSTEMS[J].Chinese Annals of Mathematics B,1999,20(2):195~204 |
| Page view： 1189
Net amount： 661 |
Authors： |
ZHOU Zixiang; |
Foundation： |
the National Research Project ``Nonlinear Science'', the Doctoral Programme Foundation of the Ministry of Eduction of China and the National Natural Science Foundation for Youth of China |
|
|
| Abstract： |
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. |
Keywords： |
Darboux transformation, Spectral parameters,
$u(p,q)$ reduction |
Classification： |
35Q51, 35Q58 |
|
|
Download PDF Full-Text
|
|
|
|
