Bianchi hypercubes and a geometric unification of the Hirota and Miwa equations

Alastair D. King, Wolfgang K. Schief

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)6842-6878
Number of pages37
JournalInternational Mathematics Research Notices
Volume2015
Issue number16
DOIs
Publication statusPublished - 20 Sep 2014

ASJC Scopus subject areas

  • Mathematics(all)

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