AKNS hierarchy and finite-gap Schrodinger potentials

TL;DR

This paper investigates the AKNS hierarchy, establishing necessary conditions for solutions and constructing finite-gap Schrödinger potentials based on these solutions.

Contribution

It provides explicit necessary conditions for functions to solve AKNS hierarchy equations and constructs finite-gap Schrödinger potentials from these functions.

Findings

Derived explicit necessary conditions for AKNS solutions

Constructed finite-gap Schrödinger potentials from AKNS solutions

Enhanced understanding of the relationship between AKNS hierarchy and Schrödinger operators

Abstract

In this paper we study AKNS hierarchy. We find explicit necessary conditions for functions $p$ and $q$ to be solution of some equation of AKNS hierarchy. Then we construct finite-gap Schrodinger potential using functions $p$ and $q$.