Averaging of nonlinearity-managed pulses.

We consider the nonlinear Schrodinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons.

Whispering gallery modes inside asymmetric resonant cavities.

Two dimensional resonators with a smooth strictly convex boundary are known to possess a whispering gallery region supporting modes concentrated near the boundary. A new class of asymmetric resonant cavities is introduced, where a whispering gallery-like region is found deep inside the resonator. The construction of such resonators is a novel application of the geometric control methods.