Non-linear Dynamics Commons^™

Studies On Lattice Systems Motivated By Pt-Symmetry And Granular Crystals, Haitao Xu

Doctoral Dissertations

This dissertation aims to study some nonlinear lattice dynamical systems arising in various areas, especially in nonlinear optics and in granular crystals. At first, we study the 2-dimensional PT-symmetric square lattices (of the discrete non-linear Schr¨odinger (dNLS) type) and identify the existence, stability and dynamical evolu- tion of stationary states, including discrete solitons and vortex configurations. To enable the analytical study, we consider the so-called anti-continuum (AC) limit of lattices with uncoupled sites and apply the Lyapunov–Schmidt reduction. Numerical experiments will also be provided accordingly. Secondly, we investigate the nonlinear waves in the granular chains of elastically inter- acting (through …