1998/06/04 by Alex Kasman, Kasman, Alex
Materials Science · Mathematics · Physics and Astronomy · #35Q53 47B39 58F07 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Magnetism in coordination complexes #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Spectral Theory (math.SP) #math-ph #math.MP #math.QA #math.SP #msc:35Q53 #msc:47B39 #msc:58F07 #nlin.SI #solv-int
paper · pdf · doi:10.48550/arxiv.math-ph/9806001
9 pages, no figures, to appear in Inverse Problems
arxiv created 1998/06/04 · openalex publication_date 1998/06/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is by now well known that the wave functions of rational solutions to the KP hierarchy (those which can be achieved as limits of the pure n-soliton solutions) satisfy an additional eigenvalue equation for ordinary differential operators in the spectral parameter. This property is known as ``bispectrality'' and has proved to be both interesting and useful. In this note, it is shown that certain (non-rational) soliton solutions of the KP hierarchy satisfy an eigenvalue equation for a non-local operator constructed by composing ordinary differential operators in the spectral parameter with translation operators in the spectral parameter, and therefore have a form of bispectrality as well. Considering the results relating ordinary bispectrality to the self-duality of the rational Calogero-Moser particle system, it seems likely that this new form of bispectrality should be related to the duality of the Ruijsenaars system.