Adiabatic invariants theory of near-integrable systems with damping

Adiabatic invariants expressed in terms of spectral data are used to integrate the non-linear Schrödinger, sine-Gordon, and 3-wave interaction equations in the presence of damping. One result, for the 3-wave interaction, is that the intensities of the three wave packets behave as though they damp separately each with its own damping constant.