Dresden 2014 – wissenschaftliches Programm

Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

DY: Fachverband Dynamik und Statistische Physik

DY 15: Nonlinear Dynamics, Synchronization and Chaos - Part I

DY 15.1: Vortrag

Mittwoch, 2. April 2014, 09:30–09:45, HÜL 186

Coherent-structure theory for non-local generalised Kuramoto-Sivashinsky eqautions — Te-Sheng Lin¹, •Dmitri Tseluiko¹, Marc Pradas², Serafim Kalliadasis², and Demetrios Papageorgiou^2,3 — ¹Department of Mathematical Sciences, Loughborough University, UK — ²Department of Chemical Engineering, Imperial College London, UK — ³Department of Mathematics, Imperial College London, UK

We analyse coherent structures in non-local active-dissipative equations, using as a prototype a generalised Kuramoto-Sivashinsky (gKS) equation with a non-local term that is assumed to be a pseudo-differential operator with a spatially independent symbol. Such equations arise in various physical contexts, e.g. in the modelling of a liquid film flow in the presence of various external effects. As for the gKS equation, we show that dispersion regularises the chaotic behaviour and the solutions evolve into arrays of interacting pulses that can form bound states. Since the Shilnikov-type approach is not applicable for analysing bound states in non-local equations, we develop a weak-interaction theory. The non-locality changes the decay of the tails of the pulses from exponential to algebraic. This has strong influence on pulse interaction and bound-state formation, e.g., unlike for local equations, for a correct description of the interaction of pulses it is not sufficient to take into account only neighbouring pulses, in addition interactions become stronger and bound-state formation is speeded up, moreover the number of possible bound states is always finite. Theoretical predictions are corroborated by numerical experiments.