Waveguide solutions for a nonlinear Schrödinger equation with mixed dispersion

Bonheure, Denis; Nascimento, Robson

Document type :

Partie d'ouvrage

DOI :

10.1007/978-3-319-19902-3_4

Title :

Waveguide solutions for a nonlinear Schrödinger equation with mixed dispersion

Author(s) :

Bonheure, Denis [Auteur]
Département de mathématiques Université Libre de Bruxelles
Quantitative methods for stochastic models in physics [MEPHYSTO]
Nascimento, Robson [Auteur]
Département de mathématiques Université Libre de Bruxelles

Book title :

Contributions to Nonlinear Elliptic Equations and Systems

Publisher :

Springer

Publication date :

2015

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]

English abstract : [en]

In this note we provide some simple results for the 4NLS model i∂tψ + ∆ψ + |ψ| 2σ ψ − γ∆ 2 ψ = 0, where γ > 0. Our aim is to partially complete the discussion on waveguide solutions in [11, Section 4.1]. In particular, we ...
Show more >In this note we provide some simple results for the 4NLS model i∂tψ + ∆ψ + |ψ| 2σ ψ − γ∆ 2 ψ = 0, where γ > 0. Our aim is to partially complete the discussion on waveguide solutions in [11, Section 4.1]. In particular, we show that in the model case with a Kerr nonlinearity (σ=1), the least energy waveguide solution ψ(t, x) = exp(iαt)u(x) with α > 0 is unique for small γ and qualitatively behaves like the waveguide solution of NLS. On the contrary, oscillations arise at infinity when γ is too large.Show less >

Language :

Anglais

Audience :

Internationale

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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