Asymptotic dynamics of certain solutions for an extended nonlinear Gross–Pitaevskii equation with critical nonlinear damping in [formula omitted

Abstract

Recent experiments have revealed the formation of stable droplets in a dipolar Bose–Einstein condensate (BEC). This surprising result has been explained experimentally by the stabilization provided by the three-body loss process that appears in the form of a critical damping term in an extended Gross–Pitaevskii equation (eGPE) to model the formation of these dipolar quantum droplets. This paper examines the dynamics of solutions to this equation (eGPE). We validate this prediction by proving that nonlinear damping prevents collapse and ensures the existence of global-in-time solutions. The asymptotic dynamics of these solutions are discussed as well, especially when the system is free (without potential). We show that all global solutions asymptotically behave as free waves in time.