Stationary solitary three-dimensional waves on a vertically flowing fluid film

Three-dimensional waves appear at the final stage of the evolving wave regime of a fluid-film flow [1]. At this stage, for values of the Reynolds number of the film flow that are sufficiently low (Re < 100), the wave regime manifests itself as a soliton gas. The film surface is covered by numerous horseshoe-shaped waves, which propagate over a thin residual layer, randomly interacting with each other and explicitly demonstrat-