New reductions of integrable matrix PDEs: $Sp(m)$-invariant systems

TL;DR

This paper introduces a novel reduction method for integrable matrix PDEs leading to new integrable systems, including derivative mKdV and Thirring models, with solutions and semi-discretizations explored.

Contribution

It proposes a new reduction technique for matrix PDEs, resulting in previously unknown integrable systems and their semi-discrete versions, along with explicit soliton solutions.

Findings

Derived new integrable coupled derivative mKdV equations.

Established a new integrable variant of the massive Thirring model.

Presented soliton solutions and semi-discretizations for the systems.

Abstract

We propose a new type of reduction for integrable systems of coupled matrix PDEs; 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 mKdV equations and a new integrable variant of the massive Thirring model, in addition to the already known systems. We also discuss integrable semi-discretizations of the obtained systems and present new soliton solutions to both continuous and semi-discrete systems. As a by-product, a new integrable semi-discretization of the Manakov model (self-focusing vector NLS equation) is obtained.