# Homework Help: Toda differential equation

1. Mar 20, 2013

### alejandrito29

toda is a chain of particles of displacement $$q(n,t)$$ acoplated by a spring

the differential equation are

$$\frac{d^2q(n,t)}{dt^2}=e^{-(q(n,t)-q(n-1,t))}-e^{-(q(n+1,t)-q(n,t))}$$

the solution for one soliton is:

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

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