Adler-Bobenko-Suris方程的连续对称约化
Continuous symmetric reductions of the Adler-Bobenko-Suris equations
摘要：
给出了Adler-Bobenko-Suris类离散可积方程的连续对称解。这些解最初由它们在相应方程所承认的两个扩展的三点广义对称性的作用下的不变性定义，它们被证明是由一个偏微分方程的可积系统确定的.建立了该系统与Nijhoff-Hone-Joshi“生成偏微分方程”的联系，构造了它的自Backlund变换和拉克斯对.应用于H1和Q1 $_{δ=0}$成员的Adler-Bobenko-Suris家庭，连续对称减少的方法产生明确的解决方案所确定的Painleve transendents。
英文摘要：
Continuously symmetric solutions of the Adler-Bobenko-Suris class of discrete integrable equations are presented. Initially defined by their invariance under the action of both of the extended three point generalized symmetries admitted by the corresponding equations, these solutions are shown to be determined by an integrable system of partial differential equations. The connection of this system to the Nijhoff-Hone-Joshi "generating partial differential equations" is established and an auto-Backlund transformation and a Lax pair for it are constructed. Applied to the H1 and Q1$_{δ=0}$ members of the Adler-Bobenko-Suris family, the method of continuously symmetric reductions yields explicit solutions determined by the Painleve trancendents.
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