The Toda lattice. II. Existence of integrals
- 15 February 1974
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 9 (4), 1924-1925
- https://doi.org/10.1103/physrevb.9.1924
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.Keywords
This publication has 6 references indexed in Scilit:
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