A determinant structure of the R I type discrete integrable system by Vinet–Zhedanov on a semi-infinite lattice is studied using the bilinear method. Bilinear equations of the R I 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 R I type discrete integrable system relates to the discrete relativistic Toda lattice.
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Mukaihira et al. (2004) studied this question.
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