Classification of optical wave solutions to the nonlinearly dispersive Schrِdinger equation

Different kinds of optical wave solutions to the nonlinearly dispersive Schrödinger equation are given according to different parameters’ regions. Those solutions include looped wave solutions, cusped wave solutions, peaked wave solutions, compacted wave solutions. The looped and cusped forms have not been reported in the literature regarding to the study of the nonlinear Schrödinger equation. We also study the limiting behavior of all periodic solutions as the parameters trend to some special values.