Dressing approach to the nonvanishing boundary value problem for the AKNS hierarchy

TL;DR

This paper introduces a dressing method-based approach to solve the nonvanishing boundary value problem for the AKNS hierarchy, utilizing vertex operators to incorporate boundary conditions effectively.

Contribution

The paper develops a novel dressing approach with vertex operators specifically designed for nonvanishing boundary conditions in integrable hierarchies.

Findings

Solutions for the AKNS hierarchy with nonvanishing boundary conditions are constructed.

The method effectively incorporates boundary conditions into the integrable system framework.

The approach broadens the applicability of the dressing method to boundary value problems.

Abstract

We propose an approach to the nonvanishing boundary value problem for integrable hierarchies based on the dressing method. Then we apply the method to the AKNS hierarchy. The solutions are found by introducing appropriate vertex operators that takes into account the boundary conditions.