Advances in Differential Equations

Well-Posedness and averaging of NLS with time-periodic dispersion management

Paolor Antonelli, ean-Claude Saut, and Christof Sparber

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Abstract

We consider the Cauchy problem for dispersion-managed nonlinear Schrödinger equations, where the dispersion map is assumed to be periodic and piecewise constant in time. We establish local and global well-posedness results and the possibility of finite time blow-up. In addition, we shall study the scaling limit of fast dispersion management and establish convergence to an effective model with averaged dispersion.

Article information

Source
Adv. Differential Equations Volume 18, Number 1/2 (2013), 49-68.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867481

Mathematical Reviews number (MathSciNet)
MR3052710

Zentralblatt MATH identifier
1261.35132

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35A01: Existence problems: global existence, local existence, non-existence 35B40: Asymptotic behavior of solutions

Citation

Antonelli, Paolor; Saut, ean-Claude; Sparber, Christof. Well-Posedness and averaging of NLS with time-periodic dispersion management. Adv. Differential Equations 18 (2013), no. 1/2, 49--68. https://projecteuclid.org/euclid.ade/1355867481.


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