KP Solitons are Bispectral
@article{Kasman1998KPSA,
title={KP Solitons are Bispectral},
author={Alex M Kasman},
journal={arXiv: Mathematical Physics},
year={1998}
}It is by now well known that the wave functions of rational solutions to the KP hierarchy which can be achieved as limits of the pure $n$-soliton solutions satisfy an 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 a recent preprint (math-ph/9806001) evidence was presented to support the conjecture that all KP solitons (including their rational degenerations) are…
References
SHOWING 1-10 OF 21 REFERENCES
Bispectral KP solutions and linearization of Calogero-Moser particle systems
- Mathematics
- 1995
Rational and soliton solutions of the KP hierarchy in the subgrassmannianGr1 are studied within the context of finite dimensional dual grassmannians. In the rational case, properties of the tau…
Bispectral commutative ordinary differential operators.
- Mathematics
- 1993
In this paper we take iip the problem of classifying bispectral linear ordinary differential operators; this problem was raised by Duistermaat and Gr nbaum [4] in connexion with some questions in…
The Bispectral Involution as a Linearizing Map
- Mathematics
- 2000
In 1975, Moser introduced the map σ to linearize the motion of the Calogero—Moser—Sutherland model with rational inverse square potential. This linearizing map was unusual in that it turned out to be…
Darboux Transformations of Bispectral Quantum Integrable Systems
- Mathematics, Physics
- 1999
We present an approach to higher-dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators.…
Differential equations in the spectral parameter
- Mathematics
- 1986
We determine all the potentialsV(x) for the Schrödinger equation (−∂x2+V(x))∅=k2∅ such that some family of eigenfunctions ∅ satisfies a differential equation in the spectral parameterk of the…
B ¨ ACKLUND-DARBOUX TRANSFORMATIONS IN SATO'S GRASSMANNIAN
- Mathematics
- 1996
We define Backlund-Darboux transformations in Sato's Grassman- nian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the…
Loop groups and equations of KdV type
- Mathematics
- 1985
On decrit une construction qui attribue une solution de l'equation de Korteweg-de Vries a chaque point d'un certain grassmannien de dimension infinie. On determine quelle classe on obtient par cette…