2017/05/31 by Andrew N. W. Hone, Theodoros E. Kouloukas, Chloe Ward · 1 citation
Physics and Astronomy · #nlin.SI
paper · pdf · doi:10.3842/sigma.2017.057
published as SIGMA 13 (2017), 057, 17 pages
arxiv created 2017/07/23 · arxiv updated 2017/07/25
The Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota-Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge transformation), defined by a triple of integers or half-integers, which produce bilinear ordinary difference equations of Somos/Gale-Robinson type. Here it is explained how to obtain Lax pairs and presymplectic structures for these reductions, in order to demonstrate Liouville integrability of some associated maps, certain of which are related to reductions of discrete Toda and discrete KdV equations.