On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2008
• Main Authors: Levi, D., Petrera, M., Scimiterna, C., Yamilov, R.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149004
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Miura Transformations and Volterra-Type Equations Associated with the Adler-Bobenko-Suris Equations / D. Levi, M. Petrera, C. Scimiterna, R. Yamilov // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 31 назв. — англ.

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 tr...