Modulational instability and two-dimensional dynamical structures

  • J. Pouget
  • M. Remoissenet
Part IV: Two-Dimensional Structures
Part of the Lecture Notes in Physics book series (LNP, volume 393)


A process of nonlinear structure formation on a two-dimensional lattice is proposed. The basic model consists of a two-dimensional lattice equipped at each node with a molecule or dipole rotating in the lattice plane. The interactions involved in the model are reduced to a periodic lattice. Such a discrete system can be applied to the problem of molecule adsorption on a substrate crystal surface, for instance. The continuum approximation of the model leads to a 2-D sine-Gordon system including nonlinear couplings, which itself can be reduced to a 2-D nonlinear Schrödinger equation in the low amplitude limit. Spatio-temporal structure formation is investigated by means of numerical simulations. These nonlinear structures are caused by modulational instabilities of initial steady states of the two-dimensional system. Moreover, the analogy between the numerically generated patterns and vortex-like excitations in a lattice is also discussed.


Continuum Approximation Nonlinear Coupling Plane Wave Solution Initial Steady State Small Amplitude Limit 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • J. Pouget
    • 1
  • M. Remoissenet
    • 2
  1. 1.Laboratoire de Modélisation en Mécanique (associé au C.N.R.S.)Université Pierre et Marie CurieParis Cédex 05France
  2. 2.Laboratoire Ondes et Structures CohérentesUniversité de BourgogneDijonFrance

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