  Under certain mode-matching conditions, small-amplitude waves can be trapped
by coupling to solitons of nonlinear fields. We present a model for this
phenomenon, consisting of a linear equation coupled to the Korteweg-de Vries
equation. The model has one parameter, a coupling constant. For one value of
the coupling constant the model becomes the linearized KdV equation. We solve
the problem exactly for a different value of the coupling parameter, for which
the solutions behave differently. We describe an application of our results to
the dynamics of molecules.
