PULSATING SELF-EXCITED WAVES.

Nonlinear quasiharmonic waves are considered in nonequilibrium systems whose lowest state is characterized by oscillatory instability. It is shown that except for one solution which possesses a nonzero topological charge, all of the known solutions describing traveling waves with a spatially modulated amplitude are unstable to small long-wave perturbations. In the case when the trivial state is unstable at high frequencies which is the case e. g. , for propagation of a planar detonation front or gasless combustion and also occasionally occurs in laser physics, a very simple nonlinear equation is proposed for describing the instability. This equation admits traveling-wave and pulsating-wave solutions which expand and contract periodically (the traveling-wave solutions are unstable with respect to perturbing waves which travel antiparallel to it). There is only one type of pulsating wave which is stable under small perturbations, and it is characterized by maximum amplitude. The results are compared with experimental observations of gasless combustion and time-dependent detonation shocks.