Advances in Differential Equations
- Adv. Differential Equations
- Volume 13, Number 1-2 (2008), 169-198.
Remarks on NLS with higher order anisotropic dispersion
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.
Adv. Differential Equations Volume 13, Number 1-2 (2008), 169-198.
First available in Project Euclid: 18 December 2012
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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.