Linear r-matrix algebra for systems separable in parabolic coordinates

J. C. Eilbeck; V. Z. Enol'skii; V. B. Kuznetsov; D. V. Leykin

Linear r-matrix algebra for systems separable in parabolic coordinates

J. C. Eilbeck, V. Z. Enol'skii, V. B. Kuznetsov, D. V. Leykin

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Abstract

We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of 2×2 matrices for the whole hierarchy, we construct the associated linear r-matrix algebra with the r-matrix dependent on the dynamical variables. A dynamical Yang-Baxter equation is discussed. © 1993.

Original language	English
Pages (from-to)	208-214
Number of pages	7
Journal	Physics Letters A
Volume	180
Issue number	3
Publication status	Published - 6 Sept 1993

Cite this

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title = "Linear r-matrix algebra for systems separable in parabolic coordinates",

abstract = "We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of 2×2 matrices for the whole hierarchy, we construct the associated linear r-matrix algebra with the r-matrix dependent on the dynamical variables. A dynamical Yang-Baxter equation is discussed. {\textcopyright} 1993.",

author = "Eilbeck, {J. C.} and Enol'skii, {V. Z.} and Kuznetsov, {V. B.} and Leykin, {D. V.}",

year = "1993",

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AU - Eilbeck, J. C.

AU - Enol'skii, V. Z.

AU - Kuznetsov, V. B.

AU - Leykin, D. V.

PY - 1993/9/6

Y1 - 1993/9/6

N2 - We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of 2×2 matrices for the whole hierarchy, we construct the associated linear r-matrix algebra with the r-matrix dependent on the dynamical variables. A dynamical Yang-Baxter equation is discussed. © 1993.

AB - We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of 2×2 matrices for the whole hierarchy, we construct the associated linear r-matrix algebra with the r-matrix dependent on the dynamical variables. A dynamical Yang-Baxter equation is discussed. © 1993.

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M3 - Article

SN - 0375-9601

VL - 180

SP - 208

EP - 214

JO - Physics Letters A

JF - Physics Letters A

IS - 3

ER -

Linear r-matrix algebra for systems separable in parabolic coordinates

Abstract

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