Statistical Mechanics of Nonlinear Dispersive Systems

The primary recurrent theme in ‘soliton physics’ as it is now evolving [1] in statistical physics, critical phenomena and condensed-matter physics generally (as well as quantum-field theory and gravity, etc.), is the simple recognition that linearization schemes are frequently misleading and (as witnessed by the contents of this Symposium) sometimes unnecessary. It is increasingly appreciated that we need to go beyond (linear) normal modes and finite-order perturbation theories in a spectrum of intrinsically nonlinear problems for which distinctive nonlinear, e.g., soliton, sectors of solution space are possible. Since the physical signatures of nonlinear modes, particularly spatially-limited ones, are often so crucial, it is essential that they are fully represented. In this situation, there is a growing tendency to develop theories which ab initio include all fundamental modes (including nonlinear ones) even if this is only possible semi-quantitatively. Such an approach has well-established precedents, e.g., phonon-roton gas models in liquid-helium-4 or vortices in superconductors.