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The nonlinearized eigenvalue problem of the Toda hierarchy in the Lie–Poisson framework

Author

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  • Du, Dianlou
  • Cao, Cewen
  • Wu, Yong-Tang

Abstract

A 3×3 discrete eigenvalue problem associated with Toda hierarchy is presented. After the nonlinearization procedure, the 3×3 discrete eigenvalue problem is turned into an integrable Poisson map on the Poisson manifold R3N with a Lie–Poisson structure. As a reduction of the Lie–Poisson structure on the co-adjoint orbit, the standard symplectic structure on the symplectic manifold R2N is obtained. The Poisson map restricted on the leaves of the symplectic foliation is reduced to a usual symplectic map, which is exactly the nonlinearized 2×2 eigenvalue problem.

Suggested Citation

  • Du, Dianlou & Cao, Cewen & Wu, Yong-Tang, 2000. "The nonlinearized eigenvalue problem of the Toda hierarchy in the Lie–Poisson framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(3), pages 332-350.
    • Handle: RePEc:eee:phsmap:v:285:y:2000:i:3:p:332-350
    DOI: 10.1016/S0378-4371(00)00236-3
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