Open AccessA CLASSICAL COMPLETELY INTEGRABLE EXTENDED SINH-CORDON SYSTEM ARISING FROM NON CONFORMALLY CONSTRAINED SL(2,R) WZNW MODEL (I)
Author(s) -
Yanshen Wang,
WenLi Yang,
Yang Huan-Xiong,
BoYu Hou
Publication year - 1994
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.43.175
Subject(s) - integrable system , trigonometry , lax pair , mathematical physics , pure mathematics , physics , lie algebra , r matrix , yang–baxter equation , matrix (chemical analysis) , mathematics , mathematical analysis , quantum , quantum mechanics , materials science , composite material
By imposing conformally broken constraints on SL(2,R) WZNW model, we obtain a new classical completely integrable system which contains the famous sinh-Gordon system as a special case. The integrability of this extended sink-Gordon system is exhibited by the existence of the Lax pair with spectral parameters. And its funda-mental .Poisson-Lie brackets can be ultralocalized, corresponding classical r-matrix depends on two spetral parameters and satisfies the classical Yang-Baxter equation. After a suitable automorphic transformation of the loop algebra on which the above Lax pair takes value, such an ultralocalized r-matrix can be classified to the so-cal-led trigonometric type of r-matrices depending essentially on one spectral parameter.