  A new algorithm is presented to find exact traveling wave solutions of
differential-difference equations in terms of tanh functions. For systems with
parameters, the algorithm determines the conditions on the parameters so that
the equations might admit polynomial solutions in tanh.
  Examples illustrate the key steps of the algorithm. Parallels are drawn
through discussion and example to the tanh-method for partial differential
equations.
  The new algorithm is implemented in Mathematica. The package
DDESpecialSolutions.m can be used to automatically compute traveling wave
solutions of nonlinear polynomial differential-difference equations. Use of the
package, implementation issues, scope, and limitations of the software are
addressed.
