Hirota-Miwa equations on a time space scale

Abstract

We derive a general time scale version of the Hirota–Miwa equation as a compatibility condition arising from a new version of a three-dimensional Lax system, construct its 3-soliton solutions, and consider various examples. We prove the invariance of the compatibility condition of the two-dimensional Lax system under a gauge transformation. The 3-soliton solution obtained here may be used in modeling in view of its variable graininess and a large number of free parameters.