title: Moving solitons in the discrete nonlinear Schrödinger equation.
abstract: Using the method of asymptotics beyond all orders, we evaluate the amplitude of radiation from a moving small-amplitude soliton in the discrete nonlinear Schrödinger equation. When the nonlinearity is of the cubic type, this amplitude is shown to be nonzero for all velocities and therefore small-amplitude solitons moving without emitting radiation do not exist. In the case of a saturable nonlinearity, on the other hand, the radiation is found to be completely suppressed when the soliton moves at one of certain isolated "sliding velocities." We show that a discrete soliton moving at a general speed will experience radiative deceleration until it either stops and remains pinned to the lattice or--in the saturable case--locks, metastably, onto one of the sliding velocities. When the soliton's amplitude is small, however, this deceleration is extremely slow; hence, despite losing energy to radiation, the discrete soliton may spend an exponentially long time traveling with virtually unchanged amplitude and speed.
authors.affiliation: Department of Maths and Applied Maths, University of Cape Town, Rondebosch 7701, South Africa. Oliver.Oxtoby@uct.ac.za
authors.forename: O F
authors.initials: OF
authors.lastname: Oxtoby
authors.forename: I V
authors.initials: IV
authors.lastname: Barashenkov