Breather solutions to the focusing nonlinear Schrödinger equation

The $N$-breather solution to the focusing nonlinear Schr\"odinger equation is presented. It is shown that the breather is linearly unstable, but the unstable modes are overstabilized and do not destroy the structure of the breather. It is also demonstrated that the breather solution can be constructed as an imbricate series of rational growing-and-decaying modes.