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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)

Abstract

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.

Keywords

Continuum Approximation Nonlinear Coupling Plane Wave Solution Initial Steady State Small Amplitude Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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