Solitons in condensed matter: A paradigm

For this new journal dealing with nonlinear phenomena we review the setting of several important current problems in the physics of condensed matter (solids, liquids). We show how the concepts embodied in the mathematical analysis of solitons provide systematic new insight (i.e., a paradigm) into a central question: what are the important physical configurations in nonlinear condensed systems? Following these general issues we summarize the analysis of the dynamics and equilibrium thermodynamics (i.e., statistical mechanics) of non-linear one-dimensional model systems, and we indicate how the solitonic configurational phenomenology provides a basis for dynamic effects which are seen both experimentally and in molecular dynamics computer simulations. Many problems in condensed matter differ from the more familiar nonlinear mechanical or hydrodynamic applications in that finite temperature thermal fluctuations must be considered along with systematic dynamics.