Quasisoliton solutions in one-dimensional anharmonic lattices. I. Influence of the shape of the pair potential

Abstract

The authors have investigated the influence of the shape of pair potentials on the existence and properties of soliton-like (quasisoliton) solutions in periodic one-dimensional lattices. The classical equations of motion were solved numerically for chains of 'atoms' with nearest-neighbour interactions. The class of pair potentials studied has the form V_sigma (r) varies as exp(-2br)-2 sigma exp(-br/ sigma ), sigma >0. For all sigma 's tested ( sigma =1, 5, 10, 15), quasisoliton solutions were observed to propagate with essentially constant velocity and survived many collisions. The most interesting conclusion is that long-lived quasisoliton solutions apparently exist for most systems with realistic anharmonic potentials. The conditions these potentials have to satisfy (a sufficiently steep, short-range repulsive part and an asymmetric (V(r+r₀) not=V(r-r₀), for all r₀) overall shape) are weak. The nature of the long-range part is unimportant. The initial conditions are more decisive; they determine the nature and behaviour of the quasisolitons created. Integrability of the Hamiltonian does not seem to be necessary for the existence of quasisolitons.