Numerical results concerning the generalized Zakharov system

  • Hichem Hadouaj
  • Gérard A. Maugin
  • Boris A. Malomed
Part VI: Mathematical Methods
Part of the Lecture Notes in Physics book series (LNP, volume 393)


A generalization of the well known Zakharov system of ionacoustic waves (Langmuir solitons) has been obtained while studying the coupling between shear-horizontal surface waves and Rayleigh surface waves propagating on top of a structure made of a nonlinear elastic substrate and a superimposed thin elastic film. The generalization consists in a nearly integrable system made of a nonlinear Schrödinger equation (thus including self-interactions) coupled to two wave equations for the secondary acoustic system (Rayleigh mode). Here we present essentially the numerical simulations pertaining to the uncoupled case (pure SH mode) and the coupled case (influence of viscous dissipation in the Rayleigh subsystem, collision of solitons).


Linear Dispersion Relation Rayleigh Surface Wave Zakharov System Rayleigh Mode Envelope Solitary Wave 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Hichem Hadouaj
    • 1
  • Gérard A. Maugin
    • 1
  • Boris A. Malomed
    • 1
  1. 1.Laboratoire de Modélisation en Mécanique associé au C.N.R.S.Université Pierre-et-Marie CurieParis Cédex 05France

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