Relations between hierarchies and inverse scattering. (English) Zbl 0839.58031
Summary: In [the author and B. Konopelchenko, Lett. Math. Phys. 28, No. 4, 307-319 (1993; Zbl 0809.58019)] it was shown how one can construct Sato hierarchies within the context of \(D\) bar dressing and a general Hirota bilinear identity, derived via \(D\) bar dressing, was shown to lead to tau functions and canonical structure for mcKP situations. In this note we will show how some spectral formulas for kernels, derived for KP in the dressing picture based on Sato hierarchies, can be further developed and embellished and related to the inverse scattering point of view. This may be seen as part of a program to bring the hierarchy picture and the scattering picture together, and understand relations between scattering data and dressing data, etc.
MSC:
| 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.) |
| 35Q58 | Other completely integrable PDE (MSC2000) |
| 35P25 | Scattering theory for PDEs |
Citations:
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