While the majority of investigations of solitary waves (solitons)
deal with continuous solutions, it is natural to seek discrete
solutions which correspond to pure, unperturbed lattices of
atoms. In rare cases such as the Toda
Lattice, analytic solutions exist for discrete systems. To
study more complex systems for which analytic solutions are not
currently available, numerical attacks have proven useful. In this
paper we present a
numerical method based on spectral methods which couples
quadratically convergent Newton-Raphson iteration with
continuation methods to generate a whole family of
lattice solitons solutions as a function of velocity.