La Ecuación de Burgers Forzada como un Modelo para Interacciones no Lineales entre Ondas Dispersivas

Abstract

The forced inviscid Burgers equation is studied as a model for the nonlinear interaction of dispersive waves. The dependent variable u(x, t) is thought of as an arbitrary mode or set of modes of a general system, and the force is tuned to mimic
the effects of other modes, which may be either near or far from resonance with u.
When the force is unimodal, a family of E'.xacttravelling waves fully describes the asymptotic behavior of the system. When the force is multimodal, with the frequencies of the various modes close to each other, the asymptotic solution is
quasi-stationary, punctuated by faster intermittent events. The existence of these "storms" may have significant implications for energy transfer among modes in more general systems.