Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities

Gadi Fibich; Xiao Ping Wang

doi:10.1016/S0167-2789(02)00626-7

Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities

Gadi Fibich, Xiao Ping Wang

School of Mathematical Sciences

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

Abstract

The stability of solitary waves for nonlinear Schrödinger equations with inhomogenous nonlinearities was discussed. As solitary waves are strongly unstable it was not possible to realize stable high-power propagation in a homogenous bulk media. It was suggested that stable high-power propagation could be achieved in plasma by sending a laser beam that created a channel with a reduced electron density.

Original language	English
Pages (from-to)	96-108
Number of pages	13
Journal	Physica D: Nonlinear Phenomena
Volume	175
Issue number	1-2
DOIs	https://doi.org/10.1016/S0167-2789(02)00626-7
State	Published - 15 Jan 2003

Keywords

Inhomogeneous nonlinearities
Nonlinear Schrödinger equation
Solitary waves
Stability

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10.1016/S0167-2789(02)00626-7

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title = "Stability of solitary waves for nonlinear Schr{\"o}dinger equations with inhomogeneous nonlinearities",

abstract = "The stability of solitary waves for nonlinear Schr{\"o}dinger equations with inhomogenous nonlinearities was discussed. As solitary waves are strongly unstable it was not possible to realize stable high-power propagation in a homogenous bulk media. It was suggested that stable high-power propagation could be achieved in plasma by sending a laser beam that created a channel with a reduced electron density.",

keywords = "Inhomogeneous nonlinearities, Nonlinear Schr{\"o}dinger equation, Solitary waves, Stability",

author = "Gadi Fibich and Wang, {Xiao Ping}",

note = "Funding Information: We thank C.F. Gui for some helpful discussions. We also thank the referees for helpful suggestions. This work is supported by an RGC Competitive Earmarked Research Grant HKUST 6176/99P. The work of G. Fibich is also partially supported by Grant No. 2000311 from the United States—Israel Binational Science Foundation (BSF), Jerusalem, Israel. ",

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AU - Fibich, Gadi

AU - Wang, Xiao Ping

N1 - Funding Information: We thank C.F. Gui for some helpful discussions. We also thank the referees for helpful suggestions. This work is supported by an RGC Competitive Earmarked Research Grant HKUST 6176/99P. The work of G. Fibich is also partially supported by Grant No. 2000311 from the United States—Israel Binational Science Foundation (BSF), Jerusalem, Israel.

PY - 2003/1/15

Y1 - 2003/1/15

N2 - The stability of solitary waves for nonlinear Schrödinger equations with inhomogenous nonlinearities was discussed. As solitary waves are strongly unstable it was not possible to realize stable high-power propagation in a homogenous bulk media. It was suggested that stable high-power propagation could be achieved in plasma by sending a laser beam that created a channel with a reduced electron density.

AB - The stability of solitary waves for nonlinear Schrödinger equations with inhomogenous nonlinearities was discussed. As solitary waves are strongly unstable it was not possible to realize stable high-power propagation in a homogenous bulk media. It was suggested that stable high-power propagation could be achieved in plasma by sending a laser beam that created a channel with a reduced electron density.

KW - Inhomogeneous nonlinearities

KW - Nonlinear Schrödinger equation

KW - Solitary waves

KW - Stability

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JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-2

ER -

Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities

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