The Lax pairs and conserved quantities of the delay Lotka-Volterra equation

Abstract

The delay Lotka-Volterra equation is a delay-differential extension of the well known Lotka-Volterra equation, and is known to have N-soliton solutions. In this paper, Backlund transformations, Lax pairs and infinite conserved quantities of the delay Lotka-Volterra equation and its discrete analogue are constructed. The conserved quantities of the delay Lotka-Volterra equation turn out to be complicated and described by using the time-ordered product of linear operators.