Stabilization of the Soliton Transported Bio-energy in Protein Molecules in the Improved Model

We study the stabilization of the solitontransported bio-energy by the dynamic equations in the improved Davydovtheory from four aspects containing the feature of free motion and states ofthe soliton at the long-time motion and at biological temperature 300 K andbehaviors of collision of the solitons by Runge-Kutta method and physicalparameter values appropriate to the $alpha$-helix protein molecules. Weprove that the new solitons can move without dispersion at a constant speedretaining its shape and energy in free and long-time motions and can gothrough each other without scattering. If considering further influence ofthe temperature effect of heat bath on the soliton, it is still thermallystable at biological temperature 300 K and in a time as long as300 ps and amino acid spacings as large as 400, which shows that the lifetime of the newsoliton is at least 300 ps, which is consistent with analytic resultobtained by quantum perturbation theory. These results exhibit that the newsoliton is a possible carrier of bio-energy transport and the improved modelis possibly a candidate for the mechanism of this transport.