The asymptotic stability of solitons in the cubic NLS equation on the line

Abstract

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.

Keywords:

• asymptotic stability
• NLS solitons
• steepest descent method

AMS Subject Classifications:

• 35Q55
• 37K15
• 37K35
• 37K40

Acknowledgments

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.