Hirota bilinear formalism and ultra-discrete singularity analysis

Ultra-discrete equations are equations in which both the dependent and independent variables can be restricted to take only integer values. In this paper, we show that it is possible to use singularity analysis to obtain the Hirota bilinear form of ultra-discrete versions of integrable equations. This method is applied to ultra-discrete Painleve equations and to integrable ultra-discrete equations in 1 + 1 dimensions.