New Estimates of the Nonlinear Fourier Transform for the Defocusing NLS Equation.
In: IMRN: International Mathematics Research Notices, Jg. 2015 (2015-09-01), Heft 17, S. 8309-8352
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Zugriff:
The defocusing NLS equation iut=-uxx + 2∣u∣²u on the circle admits a global nonlinear Fourier transform, also known as Birkhoff map, linearizing the NLS flow. The regularity properties of u are known to be closely related to the decay properties of the corresponding nonlinear Fourier coefficients. In this paper, we quantify this relationship by providing two-sided polynomial estimates of all integer Sobolev norms ∥u∥m, m⩾0, in terms of the weighted norms of the nonlinear Fourier transformed. [ABSTRACT FROM AUTHOR]
Titel: |
New Estimates of the Nonlinear Fourier Transform for the Defocusing NLS Equation.
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Autor/in / Beteiligte Person: | Molnar, Jan-Cornelius |
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Zeitschrift: | IMRN: International Mathematics Research Notices, Jg. 2015 (2015-09-01), Heft 17, S. 8309-8352 |
Veröffentlichung: | 2015 |
Medientyp: | academicJournal |
ISSN: | 1073-7928 (print) |
DOI: | 10.1093/imrn/rnu208 |
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