Advances in Differential Equations

Remarks on NLS with higher order anisotropic dispersion

Olivier Bouchel

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Abstract

We show that the introduction of third and fourth order anisotropic dispersion terms in the nonlinear Schrödinger equation enables to solve the global Cauchy problem for nonlinearities which are (super) critical in the standard case. Some blow-up results are proved in the supercritical case. Then, we prove the existence of solitary waves and discuss their regularity, their exponential decay rate at infinity, and their stability.

Article information

Source
Adv. Differential Equations Volume 13, Number 1-2 (2008), 169-198.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867363

Mathematical Reviews number (MathSciNet)
MR2482540

Zentralblatt MATH identifier
1159.35424

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B40: Asymptotic behavior of solutions 35Q51: Soliton-like equations [See also 37K40]

Citation

Bouchel, Olivier. Remarks on NLS with higher order anisotropic dispersion. Adv. Differential Equations 13 (2008), no. 1-2, 169--198. https://projecteuclid.org/euclid.ade/1355867363.


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