A Priori Estimates for the Derivative Nonlinear Schrödinger Equation

A Priori Estimates for the Derivative Nonlinear Schrödinger Equation

We prove low regularity a priori estimates for the derivative nonlinear Schrödinger equation in Besov spaces with positive regularity index conditional upon small L2-norm. This covers the full subcritical range. We use the power series expansion of the perturbation determinant introduced by Killip-V...

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Veröffentlicht in:Funkcialaj Ekvacioj 2022/12/15, Vol.65(3), pp.329-346
Hauptverfasser: Klaus, Friedrich, Schippa, Robert
Format: Artikel
Sprache:eng
Schlagworte:
A priori estimates
Conservation laws
DNLS
Estimates
Function space
Integrable PDE
Perturbation
Perturbation determinant
Power series
Regularity
Schrodinger equation
Series expansion
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Zusammenfassung:We prove low regularity a priori estimates for the derivative nonlinear Schrödinger equation in Besov spaces with positive regularity index conditional upon small L2-norm. This covers the full subcritical range. We use the power series expansion of the perturbation determinant introduced by Killip-Vişan-Zhang for completely integrable PDE. This makes it possible to derive low regularity conservation laws from the perturbation determinant.
ISSN:0532-8721
DOI:10.1619/fesi.65.329