|
Abstract: |
We show that a simple compatibility condition determines stability of WKB solutions to semilinear hyperbolic initial -value problems issued from highly oscillating initial data with large amplitudes. The compatibility condition involves the hyperbolic operator, the fundamental phase associated with the initial oscillation, and the semilinear source term; it states roughly that Interactions coecients are not too large at the resonances. The analysis relies, in the unstable case, on a Duhamel representation formula for solutions of zeroth-order pseudo-diferential equations. Our examples include coupled Klein -Gordon systems, and systems describing Raman and Brillouin instability. |
