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We use the inverse scattering transform, the auto-Bäcklund transformation, and the steepest descent method of Deift and Zhou to obtain the asymptotic stability of the solitons in the cubic NLS (nonlinear Schrödinger) equation.
S.C. was partially funded by a grant FRA 2009 from the University of Trieste and by the grant FIRB 2012 (Dinamiche Dispersive). D.P. was partially funded by the NSERC Discovery grant.
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