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We consider the cubic Szego equation perturbed by a small Toeplitz potential(natural generalization of a multiplicative potential) and having as initialcondition a soliton of the unperturbed equation. We show that the solutionpreserves the soliton shape for a long time, and we determine the effectiveODEs satisfied by the modulation parameters of the soliton.

Soliton interaction with small Toeplitz potentials for the Szego equation on the real line