与Adler-Bobenko-Suris方程相关的Miura变换和Volterra型方程
On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations
摘要：
我们构造了三浦变换，将Adler-Bobenko-Suris（ABS）列表中的可积格点方程的标量谱问题映射为Volterra型方程的离散薛定谔谱问题.我们证明了ABS方程对应于贝克隆变换的离散Krichever-Novikov方程的Yamilov（YdKN方程）的某些特殊情况。这使我们能够构造新的广义对称的ABS方程。汤加、Tsoubelis和Xenitidis对ABS方程的推广也是如此。它们都产生YdKN方程的贝克隆变换。本文构造的高阶广义对称证明了它们的可积性。
英文摘要：
We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adler-Bobenko-Suris (ABS) list into the discrete Schrödinger spectral problem associated with Volterra-type equations. We show that the ABS equations correspond to Bäcklund transformations for some particular cases of the discrete Krichever-Novikov equation found by Yamilov (YdKN equation). This enables us to construct new generalized symmetries for the ABS equations. The same can be said about the generalizations of the ABS equations introduced by Tongas, Tsoubelis and Xenitidis. All of them generate Bäcklund transformations for the YdKN equation. The higher order generalized symmetries we construct in the present paper confirm their integrability.
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