Dynamics of roll domains and the formation of structures of particles in parametric excitation of capillary waves

The proposed material is a review of the results of the study of the dynamics of roll domains of parametrically excited waves on the surface of the liquid. The processes of establishing regular wave patterns and structures from heavy particles produced by a field of standing waves are discussed from the standpoint of nonlinear dynamics.
In experimental studies, carried out over the past few years, a number of interesting results concerning the dynamics of roll domains and the formation of structures of particles at parametric excitation of capillary waves were obtained. The effect of multivariate scenarios of transition to a stable state of equilibrium was discovered, whose specific feature is that when an external signal is turned on there are various scenarios in the dynamics of competing domains at constant parameters of the system. On the surface of the liquid of high viscosity with a polygonal shape of boundaries the effect of multistability was detected, at which the existence of several stable roll regimes differing only in the orientation in space is possible. The formation of multiarmedspiral structures of heavy particles placed in a liquid layer on the surface of which capillary waves are parametrically excited was observed.
It is well known that the processes of occurrence, interaction, synchronization and destruction of spatial structures have similar dynamics in many systems (i.e., described by the same equations). But in some systems, the study of these processes can be associated with considerable difficulties. The results described in this review were obtained in the study of parametrically excited capillary ripples, which are very convenient objects for studying the pattern formation and the transition from regular structures to chaos because of its simplicity and at the same time a wide variety of observed effects. Taking this into account, we believe that the results described in the review will be important for understanding the processes taking place in various physical systems.