The asymptotic stability of solitons in the cubic NLS equation on the line
Scipio Cuccagna, Dmitry E. Pelinovsky
TL;DR
This paper proves the long-term stability of solitons in the cubic nonlinear Schrödinger equation on the line using advanced mathematical techniques.
Contribution
It introduces a novel combination of inverse scattering, auto-Backlund transformation, and steepest descent methods to establish asymptotic stability of solitons.
Findings
Confirmed asymptotic stability of solitons in cubic NLS
Developed a new analytical framework for stability analysis
Extended understanding of soliton dynamics in nonlinear PDEs
Abstract
We use the inverse scattering transform, the auto-Backlund transformation and the steepest descent method of Deift and Zhou to obtain the asymptotic stability of the solitons in the cubic NLS (nonlinear Schrodinger) equation.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Mathematical Physics Problems · Nonlinear Photonic Systems