A model for soliton dynamics on a hydrogen-bond network in helical proteins is proposed. It employs the formalism of fully integrable Toda lattices in three dimensions which admit phonons as well as solitons along the hydrogen bonds of the helices. A simulation of the three-dimensional Toda lattice system shows that the solitons are spontaneously created and are stable and moving along the helix axis. A perturbation on one of the three H-bond lines forms solitons on the other H bonds as well. The robust solitary wave may explain very long-lived modes in the frequency range of 100 cm-1 which are found in recent x-ray laser experiments. The dynamics parameters of the Toda lattice are in accordance with the usual Lennard-Jones parameters used for realistic H-bond potentials in proteins.