Nonlinear Dynamics of Particle-Like States of Multidimensional Fields
In recent five-ten years there have appeared quite a number of papers concerned with various multidimensional spatial patterns in nonlinear media: periodic and quasiperiodic lattices, localized (particle-like) solutions, spiral structures, vortices, and so on (Makhan’kov, 1983; Haken, 1983; Linde, 1984; Kuramoto, 1984). As a rule, unified methods are applied for the analysis of the structures of different origins and the results obtained can be used in different fields of physics and not only physics. This means that we witness the advent of a new field of nonlinear dynamics -the theory of structures in nonlinear media. Many problems of this theory were posed and solved before, in the theory of nonlinear waves, in the first place. However, they were, ordinarily, concerned (except, perhaps, hydrodynamics) with one- dimensional structures: solitons, shock waves, dissipative structures (combustion fronts, etc.). The inverstigation of multidimensional structures that was necessitated by astrophysics, the physics of atmosphere and ocean, the nonlinear field theory microelectronics, gave new formulations of the problems.
KeywordsLocalize Structure Nonlocalized State Gradient Form Nonlinear Schrodinger Equation Stable Equilibrium State
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