Analysis of the adiabatic limit for solitons in classical field theory

Abstract

We discuss the approximation of classical field theories by reduced systems of differential equations on the space of equilibria (the adiabatic limit). Various examples in which the approximation provides a useful description of the low-energy dynamics of solitons are discussed, including the sine-Gordon equation, the Yang–Mills–Higgs equations and the Chern–Simons–Schrödinger system. Particular emphasis is given to theorems on the validity of such approximations and proofs are given in some model cases.