Abstract
The method of singularity confinement is applied to the study of the integrability of the (discrete) Hirota-Miwa equation. We show that this equation passes the integrability test that is here adapted to the bilinear formalism. Starting from the Hirota-Miwa equation we construct a novel form for the discrete mKdV and use it to derive the discrete KdV. We obtain a trilinear form for the latter, which, however, can be reduced to a bilinear one. A novel trilinear equation is also obtained from the discrete sine-Gordon lattice.
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