Some connections between inverse scattering and solution hierarchies. (English) Zbl 0776.35063
Author’s summary: “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”.
Reviewer: A.L.Edelson (Davis)
MSC:
| 35Q51 | Soliton equations |
| 35Q58 | Other completely integrable PDE (MSC2000) |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35R30 | Inverse problems for PDEs |
| 35P25 | Scattering theory for PDEs |
Keywords:
AKNS systems; dressing kernels; Marčenko equations; algebraic and geometric points of view; inverse scattering transformReferences:
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