Soliton internal mode bifurcations: pure power law?

The bifurcation of internal solitary wave modes from the essential spectrum has been one of the most exciting recent developments in the study of soliton dynamics. To date, it was believed that the bifurcation of such modes due to discretization has a strict power law dependence on the lattice discreteness parameter. In this work we prove that this dependence actually possesses relevant exponentially small terms which distinguish between different solutions for the discrete models. The theoretical result is established by using a discrete version of the Evans function. The predictions presented herein compare very favorably with the numerical study of the linear eigenvalue problem, and offer explanations of computational effects not possible on the basis of previous theoretical studies.