On the Prediction of the Number of Solitons Excited by an Arbitrary Potential: An Observation from Inverse Scattering

A heuristic estimate for the soliton production rate by a pulse is verified for the Korteweg - de Vries equation using inverse scattering. An observation from this result, which is shown to hold for some other nonlinear equations and for the case of the 'forced' nonlinear Schroedinger equation, is that production is determined by quantities that are invariant under rescaling of the original nonlinear equations. We speculate that this result may be useful to the development of an inverse scattering theory for 'forced' nonlinear systems.