GLOBAL INSTABILITY IN FULLY NONLINEAR-SYSTEMS

Existence of a saturated steady solution of a nonlinear evolution equa tion subject to a boundary condition at x = 0, called a nonlinear glob al mode, is illustrated on the real subcritical Ginzburg-Landau model. Such a nonlinear global mode is shown to exist whereas the flow is li nearly stable, convectively unstable, or absolutely unstable. If the l inearized evolution operator is absolutely unstable, then a global mod e exists but the converse is false. This result relies only on the exi stence of a structurally unstable heteroclinic orbit in the phase spac e and is likely to be generic as demonstrated by the supercritical Gin zburg-Landau and the van der Pol-Duffing equations.