Polaron (and related) soliton concepts are based on the assumption tha
t quasiparticles are in linear interaction with harmonic oscillators.
The discrete nonlinear Schrodinger equation and its semiclassical rela
tives are also based on this assumption. Study of the effects of nonli
nearity in interaction, and anharmonicity in the restoring force of th
e oscillators, has led to notable results such as saturation of nonlin
earities and counterintuitive pheonomena such as destruction of self-t
rapping on increasing the nonlinearity. We report on these and related
results, The general aim of the investigation is to determine what po
larons owe to their harmonic (and linear) origins and how a generalize
d conceptual framework may be built which includes known polaron physi
cs as a subset. Copyright (C) 1998 Elsevier Science B.V.