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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Topological Solitons Seminar: Chaotic dynamics of phi^4 and phi^6 kinks

Presented by Yakov Shnir, Durham

8 November 2010 16:15 in CM221

We discuss new results concerning chaotic dynamics in non-perturbative sectors of the classical one-dimensional phi^4 and phi^6 models. Considering the process of production of kink-antikink pairs in the collision of particle-like states we have shown that there are 3 steps in the process, the first step is to excite the oscillon intermediate state in the particle collision, the second step is a resonance excitation of the oscillon by the incoming perturbations, and finally, the soliton-antisoliton pair can be created from the resonantly excited oscillon. It is shown that the process depends fractally on the amplitude of the perturbations and the wave number of the perturbation. We also present the effective collective coordinate model for this process.

Considering the process of the kink-antikink collisions in the one-dimensional non-integrable scalar phi6 model we reveal that,although the classical kink solutions for this model do not possess an internal vibrational model there is a resonant scattering structure of the process, thereby providing a counterexample to the common belief that existence of such a mode is a necessary condition for multi-bounce resonances in the kink-antikink collisions. We investigate the two-bounce windows in the velocity range and present evidence that this structure is entirely related to the spectrum of the bound states on the background of the combined kink-antikink configuration.

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