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Analysis of the adiabatic limit for solitons in classical field theory. (English) Zbl 1130.70013

Summary: 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, Yang-Mills-Higgs equations and Chern-Simons-Schrödinger system. Particular emphasis is given to theorems on the validity of such approximations, and proofs are given in some model cases.

MSC:

70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
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