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Dynamics of spatial structures in nonlinear optics

AuthorsGomila, Damià
AdvisorColet, Pere
KeywordsPattern formation
Localized structures
Nonlinear dynamics
Nonlinear optics
Issue DateMar-2003
PublisherUniversidad de las Islas Baleares
AbstractThe formation of spatial structures in systems out of thermodynamical equilibrium has been the subject of a large amount of scienti c research in the last quarter of the 20'th century [101, 39, 245]. Examples include patterns in hydrodynamic systems, granular media, nonlinear optics, oscillatory chemical reactions and biological systems. De nite progress has been made in the understanding of the common general theory behind the emergence and evolution of spatial structures. Methods of nonlinear dynamics and bifurcation theory such as amplitude equations, that describe the dynamics close to bifurcation points, or \phase equations", that describe the slow distortions of patterns even far from the instability threshold, have been essential tools in the development of a universal description of pattern formation and their dynamics.However, these analytical techniques have limitations, and interesting phenomena often take place beyond their range of validity. For instance, instabilities of patterns (secondary bifurcations) may take place far away from the pattern formation instability where the dynamics of the systems is not properly reproduced by the the amplitude equations obtained at the primary instability. Furthermore, amplitude equations are usually derived using the relevant modes, in general, from a Fourier decomposition, so that they are not useful to describe states without spatial periodicity such as those containing localized structures. An alternative tool is the numerical simulation of the partial di erential equations that govern the evolution of a extended system. But these numerical simulations are very time consuming and, by themselves, do not allow for a complete understanding of the dynamics of a system. For this reason, more appropriated methods of analysis have to be used and developed. Here we address this kind of problems using a powerful combination of analytical and numerical techniques.
DescriptionTesis doctoral de la Universidad de las Islas Baleares,Instituto Mediterráneo de Estudios Avanzados (IMEDEA-CSIC/UIB).-- Texto en inglés, agradecimientos en catalán.-- 181 pages, 3 appendixes.-- Fecha de lectura: 11-02-2003.
Appears in Collections:(IFISC) Tesis
(IMEDEA) Tesis
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