Elastic and inelastic collisions of interfacial solitons and integrability of two-layer fluid system subject to horizontal vibrations

We study interfacial waves in a system of two horizontal layers of immiscible inviscid fluids involved into horizontal vibrational motion. We analyze the linear and nonlinear stability properties of the solitons in the system and consider two-soliton collision scenarios. We describe the events of explosive formation of sharp peaks on the interface, which may presumably lead to the layer rapture, and find that beyond the vicinity of this peaks the system dynamics can be represented as a kinetics of a soliton gas.