16 research outputs found
Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy
We consider the extended discrete KP hierarchy and show that similarity
reduction of its subhierarchies lead to purely discrete equations with
dependence on some number of parameters together with equations governing
deformations with respect to these parameters. It is written down discrete
equations which naturally generalize the first discrete Painlev\'e equation
in a sense that autonomous version of these equations
admit the limit to the first Painlev\'e equation. It is shown that each of
these equations describes B\"acklund transformations of Veselov-Shabat periodic
dressing lattices with odd period known also as Noumi-Yamada systems of type
.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
On some integrable lattice related by the Miura-type transformation to the Itoh-Narita-Bogoyavlenskii lattice
We show that by Miura-type transformation the Itoh-Narita-Bogoyavlenskii
lattice, for any , is related to some differential-difference
(modified) equation. We present corresponding integrable hierarchies in its
explicit form. We study the elementary Darboux transformation for modified
equations.Comment: Latex, 9 page