Self-focusing in the damped nonlinear Schrödinger equation

G. Fibich

doi:10.1137/S0036139999362609

Self-focusing in the damped nonlinear Schrödinger equation

G. Fibich^*

^*Corresponding author for this work

School of Mathematical Sciences

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

93 Scopus citations

Abstract

We analyze the effect of damping (absorption) on critical self-focusing. We identify a threshold value δ_th for the damping parameter δ such that when δ > δ_th damping arrests blowup. When δ < δ_th, the solution blows up at the same asymptotic rate as the undamped nonlinear Schrödinger equation.

Original language	English
Pages (from-to)	1680-1705
Number of pages	26
Journal	SIAM Journal on Applied Mathematics
Volume	61
Issue number	5
DOIs	https://doi.org/10.1137/S0036139999362609
State	Published - 2001

Keywords

Absorption
Blowup
Collapse
Critical power
Damping
Modulation theory
Singularity

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10.1137/S0036139999362609

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abstract = "We analyze the effect of damping (absorption) on critical self-focusing. We identify a threshold value δth for the damping parameter δ such that when δ > δth damping arrests blowup. When δ < δth, the solution blows up at the same asymptotic rate as the undamped nonlinear Schr{\"o}dinger equation.",

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AB - We analyze the effect of damping (absorption) on critical self-focusing. We identify a threshold value δth for the damping parameter δ such that when δ > δth damping arrests blowup. When δ < δth, the solution blows up at the same asymptotic rate as the undamped nonlinear Schrödinger equation.

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KW - Blowup

KW - Collapse

KW - Critical power

KW - Damping

KW - Modulation theory

KW - Singularity

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Self-focusing in the damped nonlinear Schrödinger equation

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Keywords

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