Scattering for small energy solutions of NLS with periodic potential in 1D
Scipio Cuccagna, Nicola Visciglia
TL;DR
This paper proves that small energy solutions to the one-dimensional nonlinear Schrödinger equation with a periodic potential exhibit scattering behavior, indicating they disperse over time.
Contribution
It establishes the scattering result for small solutions in 1D NLS with periodic potential, a case not fully addressed before.
Findings
Small solutions scatter over time
Periodic potential does not prevent dispersion
Mathematical proof of scattering in 1D setting
Abstract
We prove scattering for small solutions to of nonlinear Schroedinger equations in 1D with a space periodic potential
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Spectral Theory in Mathematical Physics