Advanced Studies in Pure Mathematics

Stability of ground states of NLS with fourth order dispersion

Masaya Maeda

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Abstract

In this paper, we investigate the existence, uniqueness and stability of the ground states of nonlinear Schrödinger type equations with a small fourth order dispersion. Such equations appear in the higher order approximation of the propagation of laser beam in Kerr medium. We show that for the critical case, the ground state, which is unstable in the absence of the fourth order dispersion, becomes stable with small fourth order term.

Article information

Source
Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 445-452

Dates
Received: 15 December 2011
Revised: 6 February 2012
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934242

Digital Object Identifier
doi:10.2969/aspm/06410445

Mathematical Reviews number (MathSciNet)
MR3381311

Zentralblatt MATH identifier
1335.35237

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Keywords
Nonlinear Schrödinger equation standing wave orbital stability

Citation

Maeda, Masaya. Stability of ground states of NLS with fourth order dispersion. Nonlinear Dynamics in Partial Differential Equations, 445--452, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410445. https://projecteuclid.org/euclid.aspm/1540934242


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