Adiabatic transformation of continuous waves into trains of pulses

Periodic structures may grow in both conservative and dissipative systems. A multiplicity of examples can be found in nature and in the laboratory. However, periodic structures may grow and decay. We show that the effects of dissipation are essential for these structures to remain. Using the nonlinear Schrödinger equation and its extensions as basic examples of conservative and dissipative systems we show that there are two ways of adiabatic transformations of a continuous-wave solution into a train of pulses.