Amplitude equations for continuous, discrete, non-local, and stochastic nonlinear dispersive and dissipative dynamical systems
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Ioannis Giannoulis
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University of Ioannina
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Greece
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Guido Schneider
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University of Stuttgart
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Germany
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Anna Logioti
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University of Stuttgart
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Germany
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Introduction:
| | This special session brings together researchers considering problems related to deriving and justifying continuous dynamical systems, so called amplitude equations, that describe macroscopic features of dynamical systems evolving originally on a microscopic scale.
A typical macroscopic feature could be the amplitude function of a slowly modulated rapidly oscillating carrier wave. The most prominent amplitude equations in this setup are the nonlinear Schrödinger equation, the Korteweg-de Vries equation, and the Ginzburg-Landau equation. In most cases the formal derivation of the macroscopic amplitude’s evolution equation is straightforward, but its justification, proving the approximation’s validity over the slow timescale of the amplitude equation’s evolution, can be subtle depending on the setting.
Indeed, there exist counterexamples which show that the validity of such modulation equations isn’t automatically fulfilled upon their formal derivation.Recently, relevant new results have been obtained for conservation laws, degenerated systems, completely integrable systems, space-dependent systems, stochastic PDEs, lattice equations with stochastic coefficients, or non-local systems with fractional derivatives. It is the purpose of this special session to give a forum for the presentation of these new developments.
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