Spectral Difference Equations Satisfied by KP Soliton Wavefunctions

Details Spectral Difference Equations Satisfied by KP Soliton Wavefunctions Spectral Difference Equations Satisfied by KP Soliton Wavefunctions

1998-11-11

arxiv.org/abs/solv-int/9811009v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

to appear in "Inverse Problems"

Scientific paper

10.1088/0266-5611/14/6/008

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.

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