Invariant tori for a derivative nonlinear Schrödinger equation with quasi-periodic forcing.
In: Journal of Mathematical Physics, Jg. 56 (2015-03-01), Heft 3, S. 1-25
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Zugriff:
This paper is concerned with a one dimensional derivative nonlinear Schrodinger equation with quasi-periodic forcing under periodic boundary conditions iut + uxx + ig(fit)(f(|u|²)u)x = 0, x ∊ T := R/2πZ, where g(βt) is real analytic and quasi-periodic on t with frequency vector β = (β1,β2,..., βm). f is real analytic in some neighborhood of the origin in C, f (0) = 0 and f'(0) ≠ 0. We show that the above equation admits Cantor families of smooth quasi-periodic solutions of small amplitude. The proof is based on an abstract infinite dimensional Kolmogorov-Arnold-Moser theorem for unbounded perturbation vector fields and partial Birkhoff normal form. [ABSTRACT FROM AUTHOR]
Titel: |
Invariant tori for a derivative nonlinear Schrödinger equation with quasi-periodic forcing.
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Autor/in / Beteiligte Person: | Liu, Jie ; Si, Jianguo |
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Zeitschrift: | Journal of Mathematical Physics, Jg. 56 (2015-03-01), Heft 3, S. 1-25 |
Veröffentlichung: | 2015 |
Medientyp: | academicJournal |
ISSN: | 0022-2488 (print) |
DOI: | 10.1063/1.4916287 |
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