Study of Quasiperiodic Solutions of the Nonlinear Schrödinger Equation and the Nonlinear Modulational Instability

A simple and direct method is described for constructing exact quasiperiodic solutions of the focusing nonlinear Schr\"odinger equation. An algebraic constraint is imposed on the initial values of a set of auxiliary variables. The solution, expressed in terms of these auxiliary variables, is quasiperiodic in general, and represents a wider class of solutions than those obtained from the inverse-scattering transform. As an example of our method, we present solutions corresponding to a modulated plane wave.