Capillary waves in the subcritical nonlinear Schrödinger equation

In a recent article, Novoa, Michinel, and Tomasini derived a Young-Laplace equation to describe a certain class of stationary solutions of the nonlinear Schrödinger equation (NLS) with cubic and quintic nonlinearities [1]. Light beams, therefore, can sometimes take on the attribute of a liquid when propagating in nonlinear media. This occasional liquidlike nature of light was noted by several authors [2,3]. The abovementioned solutions of the NLS, on the other hand, are also used to model quantum condensates near zero temperature [4,5]. In this Brief Report, we expand the analytical results in Ref. [1] to show that the Young-Laplace equation becomes Bernoulli’s equation in the dynamical regime. The NLS with cubic-quintic nonlinearity, also called “subcritical” NLS, can be written as