Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 44, Issue 43, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/44/43/435201
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Funding
- Newton International Fellowship [NF082473]
- Royal Society [NF082473] Funding Source: Royal Society
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A sequence of canonical conservation laws for all the Adler-Bobenko-Suris (ABS) equations is derived and is employed in the construction of a hierarchy of master symmetries for equations H1-H3, Q1-Q3. For the discrete potential and Schwarzian KdV equations it is shown that their local generalized symmetries and nonlocal master symmetries in each lattice direction form centerless Virasoro-type algebras. In particular, for the discrete potential KdV, the structure of its symmetry algebra is explicitly given. Interpreting the hierarchies of symmetries of equations H1-H3, Q1-Q3 as differential-difference equations of Yamilov's discretization of Krichever-Novikov equation, corresponding hierarchies of master symmetries along with isospectral and nonisospectral zero curvature representations are derived for all of them.
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