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On Semi-Infinite Toda Chain

  • L. A. Sakhnovich
Part of the Mathematics and Its Applications book series (MAIA, volume 428)

Abstract

In this chapter the evolution law of spectral data is deduced for one nonlinear system of differential-difference equations. In particular the well-known equation
$$frac{{{d^2}x(k,t)}}{{d{t^2}}} = \exp [x(k - 1,t) - x(k,t)] - \exp [x(k,t) - x(k + 1,t)]k \geqslant 1$$
describing a chain of interacting particles (the Toda chain [62]) can be reduced to this system. Yu.Berezanski’s result [7] referring to the case of the free end when
$$x(0,t) =-\infty$$
is given here. Our general theory is also applied to the investigation of the important special case when the chain end is fixed, i.e. when
$$x(0,t) = 0$$

Keywords

Spectral Function Inverse Spectral Problem Growth Point Toda Chain Finite Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • L. A. Sakhnovich
    • 1
  1. 1.Ukrainian State Academy of CommunicationOdessaUkraine

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