Münster 1997 – scientific programme

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DY: Dynamik und Statistische Physik

DY 11: Poster I

DY 11.31: Poster

Tuesday, March 18, 1997, 14:30–17:30, F

Towards a Perturbation Scheme for Partial Differential Equations — •Wolfram Just and Frank Matthäus — Institut für Festkörperphysik, Technische Hochschule Darmstadt, Hochschulstraße 8, 64289 Darmstadt, and SFB 185

The weakly nonlinear analysis is a standard tool to investigate pattern formation beyond an instability of a spatially homogeneous state. The derivation of the corresponding reduced equations is reconsidered from the viewpoint of a formal perturbation expansion. Without restriction on the underlying partial differential equation, the explicit expression for the amplitude equation and in particular its coefficients are given for every codimension–one instability. Several important codimension–two bifurcations, including Turing–Hopf– and the degenerated soft—mode instability, are investigated along the same lines. Finally, in addition to autonomous systems, explicitly time–dependent situations are discussed. In the latter case strong resonances may lead to considerable modifications of the perturbation scheme.