On a nonlinear discretized LKR system: Reductions and underlying Virasoro symmetry algebras

Abstract

A differential-difference version of the Loewner-Konopelchenko-Rogers (LKR) system is constructed by discretization of the spatial variables in the continuous LKR system. The differential-difference LKR system admits a diversity of significant reductions. The symmetry algebras of the discrete LKR system and its reductions are shown to possess underlying Kac-Moody-Virasoro type structure. A discrete dromion-like solution of the LKR system is constructed via finite symmetry group transformation.