Classical Statistical Mechanics of Soliton-Bearing Systems

Abstract

We review the status of classical statistical mechanics for some 1-D soliton or solitary wave-bearing systems. Much of the recent activity is attributable to the motivating impact of molecular-dynamics (MD) results on discrete Φ⁴-[1–4] and sine-Gordon (sG) systems [5, 6] and the Toda lattice [7], which revealed the need for including soliton features in a statistical description, in particular, of dynamic properties. In keeping with these model systems, we discuss the evidence for kink, breather (envelope-soliton) and pulse-soli ton effects, including the associated new excitation branches. Primary attention is given to: a) thermodynamic properties and static form factors, and b) dynamic form factors (DFF) and displacement patterns.