Applications of wave equations with logarithmic nonlinearity in fluid mechanics

We apply statistical mechanics and Madelung hydrodynamical presentation for an effective description of strongly-interacting many-body systems, such as Bose liquids or Korteweg-type fluids. The logarithmic nonlinearity is shown to appear in equations describing such fluids. The resulting equations describe the irrotational and isothermal flow of a two-phase barotropic compressible inviscid fluid with internal capillarity and surface tension. We demonstrate spontaneous symmetry breaking in this class of fluids, which leads to a number of wave-mechanical and topological effects. We show the relationship between the "logarithmic" fluids and those described by polynomially nonlinear wave equations, such as the Gross-Pitaevskii one.