On MKdV Equations Related to the Affine Kac-Moody Algebra $A_{5}^{(2)}$

TL;DR

This paper derives a new integrable system of mKdV-type equations associated with the affine Lie algebra $A_{5}^{(2)}$, providing a Hamiltonian structure and analyzing its spectral properties.

Contribution

It introduces a novel integrable mKdV-type system linked to $A_{5}^{(2)}$, including Hamiltonian formulation and spectral analysis.

Findings

Derived a new integrable mKdV-type system related to $A_{5}^{(2)}$

Established Hamiltonian structure for the system

Analyzed spectral properties via Riemann-Hilbert problem

Abstract

We have derived a new system of mKdV-type equations which can be related to the affine Lie algebra $A_{5}^{(2)}$. This system of partial differential equations is integrable via the inverse scattering method. It admits a Hamiltonian formulation and the corresponding Hamiltonian is also given. The Riemann-Hilbert problem for the Lax operator is formulated and its spectral properties are discussed.