6533b872fe1ef96bd12d3768

RESEARCH PRODUCT

Modulational instability and two-dimensional dynamical structures

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description

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 Schrodinger 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.