A study of discrete nonlinear systems

An investigation of various spatially discrete time-independent non-linear models was undertaken. These models are generically applicable to many different physical systems including electron–phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler–Lagrange equation for this model is a discrete version of the Sine–Cordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics—treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasi-periodic and chaotic structures. [Continues.]