Determinant structure of non-autonomous Toda-type integrable systems

Abstract

The integrable chain of RII type by Spiridonov–Zhedanov is studied by using the bilinear method. Bilinear equations of the system are derived by applying appropriate-dependent variable transformations. A particular solution on a semi-infinite lattice is explicitly given in terms of the Casorati-type determinants. It is shown that the RII chain and the Toda-type integrable systems are connected by Bäcklund transformations.