New reductions of integrable matrix partial differential equations: Sp(m)-invariant systems

Abstract

We propose a new type of reduction for integrable systems of coupled matrix partial differential equations; this reduction equates one matrix variable with the transposition of another multiplied by an antisymmetric constant matrix. Via this reduction, we obtain a new integrable system of coupled derivative modified KdV equations and a new integrable variant of the massive Thirring model, in addition to the already known systems. We also discuss integrable semidiscretizations of the obtained systems and present new soliton solutions to both continuous and semidiscrete systems. As a by-product, a new integrable semidiscretization of the Manakov model (self-focusing vector nonlinear Schrödinger equation) is obtained.