Bianchi Hypercubes and a Geometric Unification of the Hirota and Miwa Equations

Abstract

We present a geometric and algebraic way of unifying two discrete master equations of soliton theory, namely the dKP (Hirota) and dBKP (Miwa) equations.We demonstrate that so-called Cox lattices encapsulate Bianchi (hyper)cubes associated with either simultaneous solutions of a novel 14-point and the dBKP equations or solutions of the dKP equation, depending on whether the Cox lattices are nondegenerate or degenerate.