Self-focusing with fourth-order dispersion

Gadi Fibich; Boaz Ilan; George Papanicolaou

doi:10.1137/S0036139901387241

Self-focusing with fourth-order dispersion

Gadi Fibich^*, Boaz Ilan, George Papanicolaou

^*Corresponding author for this work

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

197 Scopus citations

Abstract

We analyze self-focusing and singularity formation in the nonlinear Schrödinger equation (NLS) with high-order dispersion iψ_t±Δ^qψ+|ψ|^2σ ψ = 0, in the isotropic mixed-dispersion NLS iψ_t + Δψ + εΔ²ψ + |ψ|^2σ ψ = 0, and in nonisotropic mixed-dispersion NLS equations which model propagation in fiber arrays.

Original language	English
Pages (from-to)	1437-1462
Number of pages	26
Journal	SIAM Journal on Applied Mathematics
Volume	62
Issue number	4
DOIs	https://doi.org/10.1137/S0036139901387241
State	Published - Apr 2002

Keywords

Blowup
Critical exponent
Critical power
Gagliardo-Nirenberg inequality
Optimal constants

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abstract = "We analyze self-focusing and singularity formation in the nonlinear Schr{\"o}dinger equation (NLS) with high-order dispersion iψt±Δqψ+|ψ|2σ ψ = 0, in the isotropic mixed-dispersion NLS iψt + Δψ + εΔ2ψ + |ψ|2σ ψ = 0, and in nonisotropic mixed-dispersion NLS equations which model propagation in fiber arrays.",

keywords = "Blowup, Critical exponent, Critical power, Gagliardo-Nirenberg inequality, Optimal constants",

author = "Gadi Fibich and Boaz Ilan and George Papanicolaou",

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AU - Ilan, Boaz

AU - Papanicolaou, George

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N2 - We analyze self-focusing and singularity formation in the nonlinear Schrödinger equation (NLS) with high-order dispersion iψt±Δqψ+|ψ|2σ ψ = 0, in the isotropic mixed-dispersion NLS iψt + Δψ + εΔ2ψ + |ψ|2σ ψ = 0, and in nonisotropic mixed-dispersion NLS equations which model propagation in fiber arrays.

AB - We analyze self-focusing and singularity formation in the nonlinear Schrödinger equation (NLS) with high-order dispersion iψt±Δqψ+|ψ|2σ ψ = 0, in the isotropic mixed-dispersion NLS iψt + Δψ + εΔ2ψ + |ψ|2σ ψ = 0, and in nonisotropic mixed-dispersion NLS equations which model propagation in fiber arrays.

KW - Blowup

KW - Critical exponent

KW - Critical power

KW - Gagliardo-Nirenberg inequality

KW - Optimal constants

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JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 4

ER -

Self-focusing with fourth-order dispersion

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Keywords

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