Coupled discrete KdV equations and modular genetic networks

Abstract

We propose the analysis of a general coupled system of semidiscrete (differential–difference form) Korteweg–de Vries equations. Its integrability is proved using bilinear Bäcklund transformations and Lax pairs. Starting from the Hirota bilinear form, we construct integrable discretizations (in difference–difference form) having two different nonlinear forms. Motivation is also given by showing that a modular genetic network with activation and repression coupling between genes can be modeled by such a system.