Welcome to the DDESpecialSolutions Package for Mathematica 4.1:
By Douglas Baldwin, Unal Goktas and Willy Hereman
© 2001

SetDirectory["c:\\myDirectory"]

<<DDESpecialSolutions.m

??  DDESpecialSolutions

DDESpecialSolutions[{D[
            u[n, t],  {t, 
              2}]  ==  (1 + D[u[n, t],  t])*(u[n - 1, t] - 
                2*u[n, t] + u[n + 1, t])},  {u[n, t]},  {n, t},  {},  
      Verbose -> True,  NumericTest  ->  True,  
      SymbolicTest  ->  True]

DDESpecialSolutions[{D[
            u[n, t],  {t, 
              2}]  ==  (1 + D[u[n, t],  t])*(u[n - 1, t] - 
                2*u[n, t] + u[n + 1, t])},  {u[n, t]},  {n, t},  {},  
      InputForm -> False,  
      Verbose  ->  True,   SymbolicTest -> True]

DDESpecialSolutions[
{D[u[n, t], t] - 
            v[n, t] == 0,  
        D[v[n, t], 
              t] - (1 + v[n, t])*(u[n - 1, t] - 2*u[n, t] + 
                  u[n + 1, t]) == 0},  {u[n, t],  v[n, t]},  {n, 
        t},  {},  NumericTest -> True,  
      Verbose  ->  True]