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Homework Help: Toda differential equation

  1. Mar 20, 2013 #1
    toda is a chain of particles of displacement [tex]q(n,t)[/tex] acoplated by a spring

    the differential equation are

    [tex]\frac{d^2q(n,t)}{dt^2}=e^{-(q(n,t)-q(n-1,t))}-e^{-(q(n+1,t)-q(n,t))}[/tex]

    the solution for one soliton is:

    [tex]q= Cte+ log (\frac{1+cte2 e^{-2cte3 n + 2 sinh t}}{1+cte2 e^{-2cte3 (n+1) + 2 sinh t}} )[/tex]

    i tried various ways , for example take [tex]q(n-1,t), q(n+1,t)=cte[/tex], but, i dont obtain the solution.

    one link about this is http://www.mat.univie.ac.at/~gerald/ftp/book-jac/toda.html

    help please
     
  2. jcsd
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