Hydrodynamic properties in soliton field theory

The crucial role of hydrodynamic instabilities in soliton field theory is revealed. We demonstrate that the essential of soliton formation mechanism is the sound mode instability induced by thermodynamic instability. This instability triggers phase separation, where new thermal phases are generated to produce solitons. These solitons can be regarded as a coexistence state composed of a matter phase and a vacuum phase, with an interface providing surface tension to maintain dynamical equilibrium. The phase separation mechanism naturally allows the existence of vacuum bubbles, characterized by a vacuum phase surrounded by a matter phase with negative pressure. Furthermore, we show that the soliton interface resembles a fluid membrane, whose interface pressure satisfies a Young-Laplace-type relation, resulting in the emergence of the membrane instability induced by surface tension. In the thin-wall limit, the dispersion relation is analytically derived. This instability triggers topological transition of the interface, splitting a cylindrical interface into multiple spheres with a smaller total surface area. Such results highlight the duality between solitons and fluids, providing a field theory description for hydrodynamics with interfaces.