Compactons in strongly nonlinear lattices [Elektronische Ressource] / von Karsten Ahnert

Compactons instrongly nonlinear latticesDissertationzur Erlangung des akademischen GradesDoktor der Naturwissenschaften (Dr. rer. nat.)in der Wissenschaftsdisziplin Statistische Physik / Chaostheorieeingereicht an derMathematisch-Naturwissenschaftlichen FakultätUniversität PotsdamvonKarsten AhnertPotsdam, 2. November 2010This work is licensed under a Creative Commons License: Attribution - 3.0 Germany To view a copy of this license visit http://creativecommons.org/licenses/by/3.0/de/ Published online at the Institutional Repository of the University of Potsdam: URL http://opus.kobv.de/ubp/volltexte/2010/4853/ URN urn:nbn:de:kobv:517-opus-48539 http://nbn-resolving.org/urn:nbn:de:kobv:517-opus-48539 AbstractIn the present work, we study wave phenomena in strongly nonlinear lattices. Such lat-tices are characterized by the absence of classical linear waves. We demonstrate thatcompactons–stronglylocalizedsolitarywaveswithtailsdecayingfasterthanexponential– exist and that they play a major role in the dynamics of the system under consideration.We investigate compactons in different physical setups. One part deals with lattices ofdispersively coupled limit cycle oscillators which find various applications in natural sci-ences such as Josephson junction arrays or coupled Ginzburg-Landau equations. Anotherpart deals with Hamiltonian lattices.