The Toda lattice. II. Existence of integrals

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Abstract

Following recent computer studies which suggested that the equations of motion of Toda's exponential lattice should be completely Hénon discovered analytical expressions for the constants of the motion. In the present paper, the existence of integrals is proved by a different method. Our approach shows the Toda lattice to be a finite-dimensional analog of the Korteweg-de Vries partial differential equation. Certain integrals of the Toda equations are the counterparts of the conserved quantities of the Korteweg-de Vries equation, and the theory initiated here has been used elsewhere to obtain solutions of the infinite lattice by inverse-scattering methods.

Original languageEnglish (US)
Pages (from-to)1924-1925
Number of pages2
JournalPhysical Review B
Volume9
Issue number4
DOIs
StatePublished - Jan 1 1974

ASJC Scopus subject areas

  • Condensed Matter Physics

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