# Question:Toda Lattice Second Order Coupled Differential Equation

## Question:Toda Lattice Second Order Coupled Differential Equation

Maple
Hello, I am trying to analyze the numeric solution to the following equations - now what I want to do is a little different, I want to plot u_(n)(some number) as a function of n. This would show me the progression through the particles/distance rather than with respect to time. Here is the code: > with(DEtools): > n:=5: #(n can be as large as 500..) > > sys:=[seq(diff(u||i(t),t\$2)=exp(u||(i+1)(t)-u||i(t))-exp(u||(i)(t)-u||(i-1)(t)),i=2..n-1)]: > eqn1:=diff(u||1(t),t\$2)=exp(u||(2)(t)-u||1(t))-exp(u||(1)(t)-u||(n)(t)): > eqnn:=diff(u||n(t),t\$2)=exp(u||(1)(t)-u||n(t))-exp(u||(n)(t)-u||(n-1)(t)): > sys:=[eqn1,op(sys),eqnn]: > IC1:=[seq(u||i(0)=1,i=1..n)]: > IC2:=[seq(D(u||i)(0)=0,i=1..n)]: > IC3:=[op(IC1),op(IC2)]: > sln:=dsolve({op(sys),op(IC3)},numeric): > sln(1); Now this command will give me the values of u_n(1) and u_n'(1) but I would like to be able to plot u_(n)(1) or u_(n)(2) where n is my variable. Thank you sincerely for any help here. M. Hamilton mehamilt@up.edu
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