Integrable systems on symmetric spaces from a quadratic pencil of Lax operators

TL;DR

This paper surveys recent developments in integrable systems derived from quadratic Lax operators on Hermitian symmetric spaces, highlighting new flows, examples, and applications to higher order nonlinear Schrödinger equations.

Contribution

It provides a comprehensive overview of integrable systems from quadratic Lax pairs on symmetric spaces, including new flow types and modeling insights.

Findings

Identification of positive, negative, and rational flows

Illustration with A.III symmetric space examples

Discussion on higher order nonlinear Schrödinger equations

Abstract

The article surveys the recent results on integrable systems arising from quadratic pencil of Lax operator L, with values in a Hermitian symmetric space. The counterpart operator M in the Lax pair defines positive, negative and rational flows. The results are illustrated with examples from the A.III symmetric space. The modeling aspect of the arising higher order nonlinear Schr\"odinger equations is briefly discussed.