一个经典完全可积的非共形约束的SL（2，R）Wess－Zumino－Novikov－Witten模型（Ⅰ）

A CLASSICAL COMPLETELY INTEGRABLE EXTENDED SINH-GORDON SYSTEM ARISING FROM NON CONFORMALLY CONSTRAINED SL(2,R)WZNW MODEL(Ⅰ)

通过在ＳＬ（２，Ｒ）Ｗｅｓｓ－Ｚｕｍｉｎｏ－Ｎｏｖｉｋｏｖ－Ｗｉｔｔｅｎ（缩写为ＷＺＮＷ）模型中加入破坏共形对称性的约束，获得了一个新的经典完全可积的二维场论体系，它把著名的ｓｉｎｈ－Ｇｏｒｄｏｎ方程作为其特例。这个广义ｓｉｎｈ－Ｇｏｒｄｏｎ体系的特点是完全可积性和可超定域化，并且描写这些特点的ｒ矩阵是杨－Ｂａｘｔｅｒ方程（经典的）的一个解，它反对称，依赖于两个谱参数，但通过Ｌｏｏｐ代数的自同构变换和谱参数的重新定义后，此ｒ矩阵仍是依赖于一个谱参数的三角型ｒ矩阵。

y imposing conformally broken constraints on SL(2,R)WZNW model, we obtaina new classical completely integrable system which contains the famous sinh-Gordonsystem as a special case。The integrability of this extended sinh-Gordon system isexhibited by the existence of the Lax pair with spectral parameters.And its funda-mental Poisson-Lie brackets can be ultralocalize, corresponding classical r-matrixdepends on two spetral parameters and satisfies the classical Yang-Baxter equation。After a suitable automorphic transformation of the loop algebra on which the aboveLax 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.PACC:0220;0350;1110;0240