Moving kinks and nanopterons in the nonlinear Klein-Gordon lattice

We study moving topological solitons (kinks and antikinks) in the nonlinear Klein-Gordon chain. These solitons are shown to exist with both monotonic (non-oscillating) and oscillating asymptotics (tails). Using the pseudo-spe ctral method, the (anti)kink solutions with oscillating background (so-call ed nanopterons) are found as travelling waves of permanent profile propagat ing with constant velocity. Each of these solutions may be considered as a bound state of an (anti)kink with a background nonlinear periodic wave, so that the wave "pushes" the (anti)kink over the Peierls-Nabarro barrier. The stability of these bound states is confirmed numerically. Travelling-wave solutions of permanent profile are shown to exist depending on the convexit y of the on-site (substrate) potential. The set of velocities at which the (anti)kinks with monotonic asymptotics propagate freely is calculated. We a lso find moving non-oscillating (anti)kink profiles with higher topological charges, each of which appears to be the bound state of (anti)kinks with l ower topological charge (\Q\ = 1). (C) 2000 Elsevier Science B.V. All right s reserved.