Examples of fluid motion driven by immersed flexible structures abound in nature. In many biological settings, for instance a beating heart, an active material generates a timedependent internal forcing on the surrounding fluid. Motivated by such active biological structures, this thesis investigates parametric resonance in fluid-structure systems induced by an internal forcing via periodic mod...

It is demonstrated that optical solitons can propagate in a dispersive (or diffractive) medium with competing quadratic [i.e., chi((2))] and cubic [i.e., chi((3))] nonlinearities. Strong interplay between the nonlinearities leads to novel effects, in particular the following: (i) stable bright solitons can still exist in a self-defocusing (owing to cubic nonlinearity) medium supported by quadra...

We give an overview of the basic physical concepts and analytical methods for investigating the symmetrybreaking instabilities of solitary waves. We discuss self-focusing of spatial optical solitons in di!ractive nonlinear media due to either transverse (one more unbounded spatial dimension) or modulational (induced by temporal wave dispersion) instabilities, in the framework of the cubic nonli...

Abstract A phenomenological model of parametric surface waves (Faraday waves) is introduced in the limit of small viscous dissipation that accounts for the coupling between surface motion and slowly varying streaming and large scale flows (mean flow). The primary bifurcation of the model is to a set of standing waves (stripes, given the functional form of the model nonlinearities chosen here). ...

A phenomenological model of parametric surface waves (Faraday waves) is introduced in the limit of small viscous dissipation that accounts for the coupling between surface motion and slowly varying streaming and large-scale flows (mean flow). The primary bifurcation of the model is to a set of standing waves (stripes, given the functional form of the model nonlinearities chosen here). Our resul...

An electromagnetic wave is expected to propagate through an overdense plasma, provided that its amplitude is large enough to bring the electron motion into the relativistic regime. We study this induced transparency by using 1D and 2D particle simulations. We find that large chaotic longitudinal electric fields are generated and strong plasma heating takes place during the propagation. This beh...

A model is presented for the nonlinear interaction between a large-amplitude laser and semiconductor plasma in the semirelativistic quantum regime. The collective behavior of the electrons in the conduction band of a narrow-gap semiconductor is modeled by a Klein-Gordon equation, which is nonlinearly coupled with the electromagnetic (EM) wave through the Maxwell equations. The parametric instab...