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Photonic Crystals: Mathematical Analysis and Numerical Approximation pp 127–162Cite as

The role of the nonlinear Schrödinger equation in nonlinear optics

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Part of the book series: Oberwolfach Seminars ((OWS,volume 42))

Abstract

We explain the role of the Nonlinear Schrödinger (NLS) equation as an amplitude equation in nonlinear optics. The NLS equation is a universal amplitude equation which can be derived via multiple scaling analysis in order to describe slow modulations in time and space of the envelope of a spatially and temporarily oscillating wave packet. It turned out to be a very successful model in nonlinear optics. Here we explain its justification by approximation theorems and its role as amplitude equation in some problems of nonlinear optics.

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Authors and Affiliations

  1. Institut für Angewandte und Numerische Mathematik 2, Karlsruher Institut für Technologie, 76128, Karlsruhe, Germany

    Willy Dörfler

  2. INRIA Saclay and CMAP Ecole Polytechnique, Route de Saclay, 91128, Palaiseau Cedex, France

    Armin Lechleiter

  3. Institut für Analysis, Karlsruher Institut für Technologie, 76128, Karlsruhe, Germany

    Michael Plum

  4. Fachbereich Mathematik, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Guido Schneider

  5. Institut für Angewandte und Numerische Mathematik 3, Karlsruher Institut für Technologie, 76128, Karlsruhe, Germany

    Christian Wieners

Authors
  1. Willy Dörfler
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  2. Armin Lechleiter
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  3. Michael Plum
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  4. Guido Schneider
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  5. Christian Wieners
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Correspondence to Willy Dörfler .

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Dörfler, W., Lechleiter, A., Plum, M., Schneider, G., Wieners, C. (2011). The role of the nonlinear Schrödinger equation in nonlinear optics. In: Photonic Crystals: Mathematical Analysis and Numerical Approximation. Oberwolfach Seminars, vol 42. Springer, Basel. https://doi.org/10.1007/978-3-0348-0113-3_5

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