Spectral Difference Equations Satisfied by KP Soliton Wavefunctions
solv-int
2009-10-31 v1 Exactly Solvable and Integrable Systems
Abstract
The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring of translational operators in the spectral parameter. In the rational limit, these translational operators converge to the differential operators in the spectral parameter previously discussed as part of the theory of "bispectrality". Consequently, these translational operators can be seen as demonstrating a form of bispectrality for the non-rational solitons as well.
Cite
@article{arxiv.solv-int/9811009,
title = {Spectral Difference Equations Satisfied by KP Soliton Wavefunctions},
author = {Alex Kasman},
journal= {arXiv preprint arXiv:solv-int/9811009},
year = {2009}
}
Comments
to appear in "Inverse Problems"