Soliton interaction with small Toeplitz potentials for the Szego   equation on the real line
  We consider the cubic Szego equation perturbed by a small Toeplitz potential (natural generalization of a multiplicative potential) and having as initial condition a soliton of the unperturbed equation. We show that the solution preserves the soliton shape for a long time, and we determine the effective ODEs satisfied by the modulation parameters of the soliton. 
Oana Pocovnicu
math.AP