Generation of a stable structure of three roller domains under parametric excitation of capillary waves in a square cell with a rounded corner and a rectangular protrusion at the boundary

In nonlinear systems with instability, multistability often occurs. When studying processes occurring in real environments, the problem arises of finding paths leading to any state of equilibrium and searching for new stable states. In two-dimensional systems, they can consist of domains and differ in orientation in space. The goal of the work is to experimentally determine the features of the generation of multidomain structures in a two-dimensional system in the presence of complex boundaries of a liquid layer that experiences periodic vertical oscillations. The paper presents the results of an experimental study of the dynamics of roller domains of parametrically excited capillary waves in a square cell with a rounded corner and a rectangular protrusion at the boundary. In different domains, the rollers were oriented parallel and perpendicular to the boundaries of the cuvette and the boundaries arising near the rectangular protrusion. It was found that the dynamics of domains is determined by the movement of their fronts, and depending on the initial and boundary conditions, stable two-dimensional roller structures can appear at the edges of the cuvette with a rounded corner and a rectangular protrusion. A scenario of domain dynamics leading to the formation of a stable equilibrium state in the form of three domains has been found. In different domains, the rollers had different orientations. In this case, roundings with a large radius had the strongest effect on the dynamics of defects. Multistability of equilibrium states of roller structures was discovered, characterized by the fact that, with constant system parameters, various scenarios of domain competition arose, leading to 5 different stable equilibrium states, which differed in the number of domains, their shape and the lack of spatial symmetry. It has been experimentally shown that the most stable equilibrium states of domains arise when the rectangular protrusion is symmetrically positioned relative to the sides of the cuvette. A phenomenological model of the observed phenomenon is proposed, according to which numerical calculations are in good agreement with experiment. The results obtained may be of interest when studying the processes of establishing stable regimes in active media under strong competition and when studying the formation of two-dimensional structures from conducting particles capable of scattering electromagnetic waves.