Self-organization and nonlinear dynamics with spatially coherent structures

Abstract

In near-integrable soliton-bearing systems spatially coherent states can play an important role. In this contribution we briefly review some of the main phenomena for physically relevant situations. We start with the well-known soliton formation in integrable systems which can be interpreted as the first appearance of self-organization in physics. It is shown here that also in non-integrable Hamiltonian systems solitary waves can self-organize. For dissipative systems, the self organization hypothesis is presented and tested for 2d drift-waves. A socalled self-organization instability is found which shows the growth of a spatially coherent (solitary) structure even in the presence of turbulence. The other finding in this respect, the absence of (Anderson) localization in nonlinear disordered systems, is also briefly mentioned. The soliton, as a collective excitation, can overcome individual chaotic motion. A recent result for the proton motion in two Morse-potentials under the influence of oscillations of the heavy ions, is discussed showing the importance of solitons to create ordered structures and collective transport. Nevertheless, solitary waves can also be the constituents of deterministic (temporal) chaos as shown in the final part of this contribution.