We present a nonperturbative analysis of certain dynamical aspects of breat
hers (dispersion-managed solitons) including the effects of third-order dis
persion. The analysis highlights the similarities to and differences from t
he well-known analogous procedures for second-order dispersion. We discuss
in detail the phase-space evolution of breathers in dispersion-managed syst
ems in the presence of third-order dispersion. (C) 2001 Optical Society of
America.