Two hierarchies of new generalized multicomponent AKNS-type soliton equations

TL;DR

This paper introduces two new multicomponent generalizations of AKNS-type spectral problems, constructs associated soliton hierarchies, and proves their Liouville integrability using bi-Hamiltonian structures.

Contribution

It presents novel multicomponent AKNS-type spectral problems and establishes their integrability through bi-Hamiltonian structures and recursion operators.

Findings

Two new hierarchies of soliton equations are constructed.

Bi-Hamiltonian structures are established for each hierarchy.

Liouville integrability is proven for all systems in the hierarchies.

Abstract

Two multicomponent generalizations of the AKNS-type spectral problems associated with $sl(2,\mathbb{R})$ and $so(3,\mathbb{R})$ are introduced and the corresponding two hierarchies of generalized multicomponent AKNS-type soliton equations are presented by the standard procedure, respectively. By virtue of the trace identity, bi-Hamiltonian structures which lead to a common recursion operator are established for each of the two resulting soliton hierarchies. And thus the Liouville integrability is shown for all systems in each of the two new generalized soliton hierarchies, seperately.