On Semi-Infinite Toda Chain

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


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
$$x(0,t) = 0$$


Spectral Function Inverse Spectral Problem Growth Point Toda Chain Finite Chain 
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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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