The homogeneous realization of the basic representation of Ainf1sup(1) and the toda lattice

A. P.E. Ten Kroode; M. J. Bergvelt

doi:10.1007/BF00416464

The homogeneous realization of the basic representation of A_inf1^sup(1) and the toda lattice

A. P.E. Ten Kroode, M. J. Bergvelt

Mathematics

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Abstract

It is well-known that the principal realization of the basic module L(Λ₀) over A_inf1^sup(1)gives rise to the KdV hierarchy of partial differential equations. Here we use the homogeneous realization of the same module to construct a hierarchy of differential-difference equations, the first member of which turns out to be the equation for the Toda lattice.

Original language	English (US)
Pages (from-to)	139-147
Number of pages	9
Journal	Letters in Mathematical Physics
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/BF00416464
State	Published - Aug 1986

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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title = "The homogeneous realization of the basic representation of Ainf1sup(1) and the toda lattice",

abstract = "It is well-known that the principal realization of the basic module L(Λ0) over Ainf1sup(1)gives rise to the KdV hierarchy of partial differential equations. Here we use the homogeneous realization of the same module to construct a hierarchy of differential-difference equations, the first member of which turns out to be the equation for the Toda lattice.",

author = "{Ten Kroode}, {A. P.E.} and Bergvelt, {M. J.}",

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AU - Bergvelt, M. J.

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N2 - It is well-known that the principal realization of the basic module L(Λ0) over Ainf1sup(1)gives rise to the KdV hierarchy of partial differential equations. Here we use the homogeneous realization of the same module to construct a hierarchy of differential-difference equations, the first member of which turns out to be the equation for the Toda lattice.

AB - It is well-known that the principal realization of the basic module L(Λ0) over Ainf1sup(1)gives rise to the KdV hierarchy of partial differential equations. Here we use the homogeneous realization of the same module to construct a hierarchy of differential-difference equations, the first member of which turns out to be the equation for the Toda lattice.

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The homogeneous realization of the basic representation of A_inf1^sup(1) and the toda lattice

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