Research objectives and content
This project aims at a better understanding for the role of discrete breathers in the dynamics of nonlinear lattices. We propose to investigate, analytically and numerically, the long-time dynamics of perturbed breather solutions, and thereby gaining insight into the possible mechanisms for breather growth and decay and their spontaneous creation and destruction at finite temperatures. Furthermore, we aim at an increased understanding of breather dynamics close to instability thresholds, and in particular we plan to investigate the possibility of switching between breathers with different properties (e.g. mobile o' immobile) by the application of small external perturbations. Switching between pinned and mobile breathers is of interest ir descriptions of storage and transport of vibrational energy in biological macromolecules, and is also expected to have technological applications. We propose to study enharmonic 1attices with long-range interaction as candidates for systems where multistability of breathers and switching can be expected. Also fundamental properties (e.g. spatial decay) of breather! in lattices with long-range interactions will be investigated. Training content (objective, benefit and expected impact)
I expect to acquire a deeper knowledge and wider competence in the subject of nonlinear localization in discrete system concerning understanding of the fundamental mathematical techniques as well as experience with the numeric, implementation of these ideas.