EFFECT OF NONLOCAL INTERACTIONS ON SOLITON DYNAMICS IN ANHARMONIC CHAINS - SCALE COMPETITION

We consider the effect of a harmonic non-local interaction potential i n a chain with short-range anharmonicity, The existence of two velocit y dependent competing length scales leads to two types of solitons wit h characteristically different widths and shapes for two velocity regi ons separated by a gap. The low-velocity branch exists up to a maximum critical velocity where the solitary-wave shape reaches a crest-like form. Using direct perturbation methods and a quasicontinuum approxima tion with the appropriate scale we obtain accurate analytic expression s, Using near threshold stability analysis we find that the crest soli ton solution is unstable. In the high-velocity branch we use the multi ple scale analysis since two different scales are important in the cen tre and the tail of the solitary wave, respectively. Here a qualitativ e agreement is obtained.