Our research focuses on analytical modeling of non-linear interaction between ensembles of liquid droplets and the analysis of nonlinear wave phenomena emerging in such configurations. The system under consideration comprises of continuous two-phase flow with disc-shaped droplets driven by a pressure gradient in the narrow gap between two parallel surfaces. We examine cases with negligible inertial effects where the viscosity of the droplet is negligible in comparison with the viscosity of the surrounding fluid. We initially present analytical derivation of the governing equations of motion using Hele-Shaw flow approximation, governed by the 2D Laplace equation, with multiple, static and dynamic droplets. Nonlinear analysis of 1D and 2D lattice is derived and utilized to develop an analytical description of various localized and spatially extended solutions and study their stability properties and possible bifurcations.
