I will review the intermediate long wave equation which interpolates between the celebrated Korteweg-de Vries and Benjamin-Ono equations, describing the one-dimensional waves in a shallow and deep water, respectively. The quantum version of this equation is of some interest to the theory of quantum wires and other quasi-one dimensional condensed matter systems. I will explain the unexpected connection of this equation to the dynamics of gauge theories in two, four, and six dimensions. This connection is one of the applications of the BPS/CFT correspondence. Based on the work in progress with Andrei Okounkov