Micro- and Macro-scale Self-organization in a Dissipative Plasma

We study a nonlinear three-wave interaction in an open dissipative model of stimulated Raman backscattering in a plasma. A hybrid kinetic-fluid scheme is proposed to include anomalous kinetic dissipation due to electron trapping and plasma wave breaking. We simulate a finite plasma with open boundaries and vary a transport parameter to examine a route to spatio-temporal complexity. An interplay between self-organization at micro (kinetic) and macro (wave/fluid) scales is revealed through quasi-periodic and intermittent, evolution of dynamical variables, dissipative structures and related entropy rates. An evidence that entropy rate extrema correspond to structural transitions is found

Higher electron non-linearities in the dynamics of langmuir collapse

We derive a set of generalized Zakharov equations valid for both electrostatic and electromagnetic, that is, potential and non-potential, perturbations which include corrections due to higher electron non-linearities and allowing for a breakdown of slow-time scale quasi-neutrality and we show how these correction terms may halt the Langmuir collapse in two or three dimensions

On Origin and Dynamics of the Discrete NLS Equation

"We investigate soliton-like dynamics in the descrete nonlinear Schroedinger equation (DNLSE) describing the generic 3-element descrete nonlinear system with a dispersion. The DNLSE (1+2) is solved on the 3 x N descrete lattice, where N is the variable number introduced through the descretized dispersion term. In quasi-linear and strongly nonlinear regimes the evolution shows robustness with respect to the N variation. However, the intermediate regime often exhibiting chaos, appears highly sensitive to the number of descrete points, making an exact solving of the DNLSE (1+2) a dubious task. We briefly outline implications on other continuum models alike the NLSE.

Modulation Instability in Two-dimensional Nonlinear Schrodinger Lattice Models with Dispersion and Long-range Interactions

"The problem of modulation instability of continuous wave and array soliton solutions in the framework of a two-dimensional continuum-discrete nonlinear Schrodinger lattice model which accounts for dispersion and ling-range interactIONS BETWEEN ELEMENTS, IS INVESTIGATED. APPLICATION OF THE LINEAR STABILITY ANALYSIS BASED ON AN ENERGETIC PRINCIPLE AND A VARIATIONAL APPROACH, WHICH WERE ORIGINALLY DEVELOPED FOR THE CONTINUUM NONLINEAR SCHRODINGER MODEL, IS PROPOSED. Analytical expressions for the corresponding instability thresholds and the growth rate spectra are calculated.