TL;DR
This paper proves that in the radial case, solutions of the nonlinear Schrödinger equation with finite energy converge to a soliton as they evolve over time.
Contribution
It provides a geometric characterization of solitons by demonstrating convergence of solutions to solitons in the radial case.
Findings
$H^1$ solutions converge to solitons
Convergence holds for radial solutions
Provides geometric insight into soliton behavior
Abstract
I show that solutions of the nonlinear Schroedinger equation which are incoming converge to a soliton, in the radial case.
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Taxonomy
TopicsAdvanced Topics in Algebra