Soliton internal mode bifurcations: Pure power law? art. no. 036602

The bifurcation of internal solitary wave modes from the essential spectrum has been one of the most exciting recent developments in the study of soli ton dynamics. To date, it was believed that the bifurcation of such modes d ue to discretization has a strict power law dependence on the lattice discr eteness parameter. In this work we prove that this dependence actually poss esses relevant exponentially small terms which distinguish between differen t solutions for the discrete models. The theoretical result is established by using a discrete version of the Evans function. The predictions presente d herein compare very favorably with the numerical study of the linear eige nvalue problem, and offer explanations of computational effects not possibl e on the basis of previous theoretical studies.