STEEP NONLINEAR GLOBAL MODES IN SPATIALLY DEVELOPING MEDIA

A new frequency selection criterion valid in the fully nonlinear regim e is resented for extended oscillating states in spatially developing media. The spatial structure and frequency of these modes are dominate d by the existence of a sharp front connecting linear to nonlinear reg ions. A new type of fully nonlinear time harmonic solutions called ste ep global modes is identified in the context of the supercritical comp lex Ginzburg-Landau equation with slowly spatially varying coefficient s. A similar formulation is likely to be applicable to fully nonlinear synchronized global oscillations in spatially developing free shear f lows. (C) 1998 American Institute of Physics.