Determinant structure of<i>R_I</i>type discrete integrable system

Abstract

A determinant structure of the RI type discrete integrable system by Vinet–Zhedanov on a semi-infinite lattice is studied using the bilinear method. Bilinear equations of the RI type discrete integrable system are derived by applying appropriate dependent variable transformations. It is shown that a particular solution for the bilinear equations on a semi-infinite lattice is given in terms of Casorati-type determinants. It is also discussed how the RI type discrete integrable system relates to the discrete relativistic Toda lattice.