A class of models long waves in dispersive media with coupled quadratic nonlinearities on a periodic domain $\mathbb{T}$ are studied. We used two distributed controls, supported $\omega\subset\mathbb{T}$ and assumed to be generated by linear feedback law conserving the "mass" (or "volume"), prove global control results. The first result, using spectral analysis, guarantees that system considera...

The comparative analysis of the dynamic holograms recording efficiency in media with non-resonance mechanisms of optical nonlinearity is carried out. It is showed that the greatest values of this parameter are provided by thermodiffusion and electrostrictive mechanisms of concentration nonlinearity of liquid dispersed media.

[1] How often does a contaminant ‘particle’ migrating in a porous medium set a distance record, i.e., advance farther from the origin than at all previous time steps? This question is of fundamental importance in characterizing the nature of the leading edge of a contaminant plume as it is transported through an aquifer. It was proven theoretically by Majumdar and Ziff (2008) that, in the 1d ca...

We introduce a real-space technique able to extend the standard Hopfield approach commonly used in quantum polaritonics to the case of inhomogeneous lossless materials interacting with the electromagnetic field. We derive the creation and annihilation polaritonic operators for the system normal modes as linear, space-dependent superpositions of the microscopic light and matter fields. We prove ...