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Weakly Nonlinear Wave Packets and the Nonlinear Schrödinger Equation

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Nonlinear Waves in Fluids: Recent Advances and Modern Applications

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 483))

Abstract

This chapter describes weakly nonlinear wave packets. The primary model equation is the nonlinear Schrödinger (NLS) equation. Its derivation is presented for two systems: the Korteweg-de Vries equation and the water-wave problem. Analytical as well as numerical results on the NLS equation are reviewed. Several applications are considered, including the study of wave stability. The bifurcation of waves when the phase and the group velocities are nearly equal as well as the effects of forcing on the NLS equation are discussed. Finally, recent results on the effects of dissipation on the NLS equation are also given.

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Author information

Authors and Affiliations

  1. Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan, Cachan, France

    Frédéric Dias

  2. Department of Mathematics and Statistics, University of Surrey, Guildford, UK

    Thomas Bridges

Authors
  1. Frédéric Dias
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  2. Thomas Bridges
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Editors and Affiliations

  1. Loughborough University, UK

    Roger Grimshaw

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Dias, F., Bridges, T. (2005). Weakly Nonlinear Wave Packets and the Nonlinear Schrödinger Equation. In: Grimshaw, R. (eds) Nonlinear Waves in Fluids: Recent Advances and Modern Applications. CISM International Centre for Mechanical Sciences, vol 483. Springer, Vienna. https://doi.org/10.1007/3-211-38025-6_2

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  • DOI: https://doi.org/10.1007/3-211-38025-6_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-25259-8

  • Online ISBN: 978-3-211-38025-3

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