6533b872fe1ef96bd12d3581
RESEARCH PRODUCT
Attraction d'ondes pour des systèmes à résonance d'ondes contra-propagatives
Muriel Greniersubject
RésonanceLong time behaviour[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM]Comportement asymptotiqueInitial boundary value problem[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Hyperbolic PDEResonanceCounter-propagating waves[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]Wave attractionEDP hyperbolique avec conditions initiales et aux bordsOndes contra-propagativesAttraction d'ondesdescription
Wave attraction in counter-propagating waves systems is a general phenomenon that was first established in Physics in the context of the attraction of the polarization between two counter-propagating waves in optical fibers. This phenomenon has been observed experimentally, and its properties were studied through numerical simulations. The models are Hamiltonian hyperbolic systems of partial differential equations, with time-dependent boundary conditions on a finite interval. The underlying mechanism can be traced back to the existence of singular tori in the corresponding stationary equations. In this work we analyze in detail the simplest example in this family of models. We show that most of the phenomena of the wave attraction process are already present in a linear model with resonant interaction. We establish the existence and regularity of the solutions and analyze the relaxation towards a stationary solution that features the wave attraction properties.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-10-26 |