Hirota bilinear formalism and ultra-discrete singularity analysis

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Published 10 March 2009 • 2009 IOP Publishing Ltd and London Mathematical Society
, , Citation N Joshi et al 2009 Nonlinearity 22 871 DOI 10.1088/0951-7715/22/4/010

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Author affiliations

1 School of Mathematics and Statistics F07, University of Sydney, NSW2006 Sydney, Australia

2 Department of Mathematics, College of Charleston, 175 Calhoun street, RSS room 339, Charleston, SC, 29424, USA

3 Centre de Physique Théorique, Ecole Polytechnique, CNRS, 91128 Palaiseau, France

Dates

  1. Received 13 August 2008
  2. Published

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0951-7715/22/4/871

Abstract

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 Painlevé equations and to integrable ultra-discrete equations in 1 + 1 dimensions.

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