Weakly Nonlinear Wave Packets and the Nonlinear Schrödinger Equation

  • Frédéric Dias
  • Thomas Bridges
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 483)


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.


Solitary Wave Group Velocity Water Wave Wave Train Homoclinic Solution 


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Copyright information

© CISM, Udine 2005

Authors and Affiliations

  • Frédéric Dias
    • 1
  • Thomas Bridges
    • 2
  1. 1.Centre de Mathématiques et de Leurs ApplicationsEcole Normale Supérieure de CachanCachanFrance
  2. 2.Department of Mathematics and StatisticsUniversity of SurreyGuildfordUK

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