We introduce a novel generalization of the discrete nonlinear Schrodinger equation that supports solitons that can describe how proteins are folded. As an example we scrutinize the villin headpiece HP35, an archetypal protein for testing both experimental and theoretical approaches to protein folding. Using its protein backbone as a template we explicitely construct two solitons that model over 7.000 secondary superstructures in the Protein Data Bank with an atomary level accuracy of 1.0 Angstrom or less.