Toda lattice and Korteweg de Vries relation

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The discussion focuses on the relationship between the Toda lattice and the Korteweg de Vries (KdV) equation, emphasizing the former as a finite-dimensional counterpart to the latter. A recommended resource is M. Toda's book "Theory of Nonlinear Lattices" from 1981, which provides valuable insights. Additionally, the initial identification of this relationship was made by Flaschka in 1974, with relevant details found in his article published in Physical Review B. These references are essential for understanding the connections between these two mathematical constructs. The Toda lattice and KdV equation are crucial in the study of integrable systems and nonlinear dynamics.
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Does anybody know where I can find a good reference which describes in a simple way the relations between the Toda lattice and the Korteweg de Vries equation and in particular the former as the finite-dimensional equivalent of the latter?
 
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Relation of Toda and Kdv

A good place to start is the book by M. Toda
 
Thank you, the book "Theory of nonlinear lattices" (1981) has been indeed helpful.

I have also found out that the relationship was first pointed out by Flaschka in 1974 and should be described in on of his articles (Phys. Rev. B 9, 1924–1925 (1974), http://prola.aps.org/abstract/PRB/v9/i4/p1924_1).
 

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