The integrable Ermakov structure and elliptic vortex solution in the inviscid gas-liquid two-phase flow

Abstract

The inviscid gas-liquid two-phase flow is an important physical model, which has a wide range of applications in natural, engineering and biomedicine. In this paper, we propose a novel elliptic vortex ansatz and thereby reduce the gas-liquid two-phase flow to a set of nonlinear dynamical system. The latter is shown to not only admit the Lax pair formulation and associated integrable stationary nonlinear Schrödinger connection, but also possess the integrable Ermakov structure of Hamiltonian type which exists both in the density parameters and mixed velocity of the two-phase flow. In addition, we construct a class of vortex solutions termed pulsrodons corresponding to pulsating elliptic warm-core rings and discuss its dynamical behaviors. Such solutions have recently found applications in geography, tidal oscillations, oceanic and atmospheric dynamics.