title: Spatial and temporal structures in cavities with oscillating boundaries.
abstract: We review the general features of particles, waves and solitons in dynamical cavities formed by oscillating cavity mirrors. Considered are the dynamics of classical particles in one-dimensional geometry of a dynamical billiard, taking into account the non-elastic collisions of particles with mirrors, the (quasi-energy) states of a single quantum particle in a potential well with periodically oscillating wells, and nonlinear structures, including nonlinear Rabi oscillations, cavity optical solitons and solitons of Bose-Einstein condensates, in dynamical cavities or traps.
authors.affiliation: Theoretical Department, Vavilov State Optical Institute, St Petersburg 199053, Russia Laser Optics, ITMO University, St Petersburg 197101, Russia Laboratory of Atomic Radiospectroscopy, Ioffe Physical Technical Institute, St Petersburg 194021, Russia nrosanov@yahoo.com.
authors.forename: Nikolay N
authors.initials: NN
authors.lastname: Rosanov
authors.affiliation: Theoretical Department, Vavilov State Optical Institute, St Petersburg 199053, Russia.
authors.forename: George B
authors.initials: GB
authors.lastname: Sochilin
authors.affiliation: Theoretical Department, Vavilov State Optical Institute, St Petersburg 199053, Russia.
authors.forename: Vera D
authors.initials: VD
authors.lastname: Vinokurova
authors.affiliation: Theoretical Department, Vavilov State Optical Institute, St Petersburg 199053, Russia.
authors.forename: Nina V
authors.initials: NV
authors.lastname: Vysotina
keywords: Bose–Einstein condensate; cavity solitons; dynamical billiard; dynamical trap; quantum particles