Steady state solutions for nonlinear Schrödinger equation arising in optics

Yisong Yang; Ruifeng Zhang

doi:10.1063/1.3122774

Steady state solutions for nonlinear Schrödinger equation arising in optics

Yisong Yang, Ruifeng Zhang

Mathematics

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

Abstract

In this paper, we use the method of calculus of variations to develop an existence theory for the steady state solutions of a nonlinear Schrödinger equation modeling light waves propagating in a photorefractive crystal. We show via direct minimization and mountain-pass argument that there exist steady state solutions realizing a continuous spectrum of energy points or wavenumbers.

Original language	English (US)
Article number	053501
Journal	Journal of Mathematical Physics
Volume	50
Issue number	5
DOIs	https://doi.org/10.1063/1.3122774
State	Published - 2009

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.3122774

Cite this

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title = "Steady state solutions for nonlinear Schr{\"o}dinger equation arising in optics",

abstract = "In this paper, we use the method of calculus of variations to develop an existence theory for the steady state solutions of a nonlinear Schr{\"o}dinger equation modeling light waves propagating in a photorefractive crystal. We show via direct minimization and mountain-pass argument that there exist steady state solutions realizing a continuous spectrum of energy points or wavenumbers.",

author = "Yisong Yang and Ruifeng Zhang",

note = "Funding Information: Y.Y. was supported in part by the National Science Foundation and R.Z. was supported in part by the Natural Science Foundation of Henan Education Department (Grant No. 2008A110002) and the Natural Science Foundation of Henan University (Grant No. 06YBZR027).",

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PY - 2009

Y1 - 2009

N2 - In this paper, we use the method of calculus of variations to develop an existence theory for the steady state solutions of a nonlinear Schrödinger equation modeling light waves propagating in a photorefractive crystal. We show via direct minimization and mountain-pass argument that there exist steady state solutions realizing a continuous spectrum of energy points or wavenumbers.

AB - In this paper, we use the method of calculus of variations to develop an existence theory for the steady state solutions of a nonlinear Schrödinger equation modeling light waves propagating in a photorefractive crystal. We show via direct minimization and mountain-pass argument that there exist steady state solutions realizing a continuous spectrum of energy points or wavenumbers.

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Steady state solutions for nonlinear Schrödinger equation arising in optics

Abstract

ASJC Scopus subject areas

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