Spatiotemporal Properties of Coupled Nonlinear Oscillators

Spatiotemporal properties of classical coupled nonlinear oscillators are investigated in this thesis. Chapter 1 gives an introduction to nonlinear lattices and to the concept of breathers, that are spatially localized and temporally periodic excitation in nonlinear lattices. The concept of anti-continuous limit that provides the basic methodology in probing spatiotemporal breather properties is discussed. In Chapter 2, the general approach for finding exact breather solutions from the anti-continuous limit is examined, and the rotating wave approximation(RWA) is applied to probe the spatial structure of static breathers. Numerical evidence reveals that the RWA relates the spatial structure of stable multi-breathers to a single breather of the same frequency. Chapter 3 presents linear stability analysis of static breathers and gives a systematic way to construct mobile breathers. Formation and collision properties of this moving breathers are also studied. Chapter 4 discusses dynamics of kinks and anti-kinks in hydrogen-bonded chains in the context of two-component soliton model. From molecular dynamics simulations with finite temperature, it is observed that, in a real system (eg. ice), a pair of kink and anti-kink can evolve into a moving-breather-like excitation. Chapter 5 is devoted to the understand of the effects of disorder in the Holstein model. The summary is given in Chapter 6.