Some connections between inverse scattering and solution hierarchies

Abstract

Canonical asymptotic expressions for AKNS wave matrices involving tau functions based on continuous spectrum are related to the appropriate dressing gauge transformations via hierarchy considerations and asymptotics for continuous spectrum situations. In a continuous spectrum context determinant constructions of dressing kernels and tau functions, completeness relations, Marčenko equations, the structure of kernels, and the Grassmannian formulation are investigated.

Keywords:

• Inverse scattering
• AKNS systems
• dressing kernels
• solution hierarchies
• Marčenko equations

AMS:

• 35Q51
• 35Q58
• 58F07