We study focussing discrete nonlinear Schr\"{o}dinger equations and present a
new variational existence proof for homoclinic standing waves (bright
solitons). Our approach relies on the constrained maximization of an energy
functional and provides the existence of two one-parameter families of waves
with unimodal and even profile function for a wide class of nonlinearities.
Finally, we illustrate our results by numerical simulations.Comment: new version with revised introduction and improved condition (A3); 16
pages, several figure
