Multicomponent Fokas-Lenells equations on Hermitian symmetric spaces

TL;DR

This paper develops multi-component integrable Fokas-Lenells equations on Hermitian symmetric spaces, detailing their structures, reductions, and examples across classical types, advancing the understanding of their integrability and nonlocal models.

Contribution

It introduces new multi-component Fokas-Lenells equations on Hermitian symmetric spaces, including their Lax pairs, bi-Hamiltonian structures, and reductions, expanding the class of integrable models.

Findings

Formulated multi-component Fokas-Lenells equations for various symmetric spaces

Provided Lax and bi-Hamiltonian structures for these equations

Explored reductions leading to nonlocal integrable models

Abstract

Multi-component integrable generalizations of the Fokas-Lenells equation, associated with each irreducible Hermitian symmetric space are formulated. Description of the underlying structures associated to the integrability, such as the Lax representation and the bi-Hamiltonian formulation of the equations is provided. Two reductions are considered as well, one of which leads to a nonlocal integrable model. Examples with Hermitian symmetric spaces of all classical series of types A.III, BD.I, C.I and D.III are presented in details, as well as possibilities for further reductions in a general form.