Analytic method for finding stationary solutions to generalized nonlinear Schrödinger equations

We present a method to generate analytic, stationary solutions to generalized nonlinear Schrödinger equations with complicated dispersion profiles. The experimental observation of such solutions in a fibre laser was recently reported. Our method proceeds in a systematic fashion and does not require initial guesses. The solutions take the form of an exponentially converging sum of functions, each with an infinite number of discontinuous derivatives at the origin, which disappear upon upon summation. They can be found conveniently using a symbolic manipulation program. Our method can not only find stable solitons, but also higher order solutions that tend to be unstable and that are difficult to find numerically.