Abstract
As an application of the theory of infinite-dimensional Grassmannians and the representation theory of gl 1 we shall study in this chapter certain nonlinear “exactly solvable” systems of differential equations. Exactly solvable means here that the nonlinear system can be transformed to an (infinite-dimensional) linear problem. A prototype of the equations is the Korteweg-de Vries equation
. It turns out that it is more natural to consider an infinite system of equations like that above, for obtaining explicit solutions. The set of equations is called the KdV hierarchy and it can be derived from another set of equations, the KP (Kadomtsev-Petviashvili) hierarchy. The Grassmannian approach can be more directly applied to the KP hierarchy and therefore we shall mainly consider the KP case.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer Science+Business Media New York
About this chapter
Cite this chapter
Mickelsson, J. (1989). The Kp Hierarchy. In: Current Algebras and Groups. Plenum Monographs in Nonlinear Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-0295-8_11
Download citation
DOI: https://doi.org/10.1007/978-1-4757-0295-8_11
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-0297-2
Online ISBN: 978-1-4757-0295-8
eBook Packages: Springer Book Archive