Classification of optical wave solutions to the nonlinearly dispersive Schrödinger 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.

► We study the existence of more fantastic optical wave solutions.
► Our results show that the solutions are influenced by the nonlinear strength and the sign of parameters.
► A geometric method is applied to determine all possible solutions.
► The parameter space is divided in further details.
► The limit behavior of all periodic solutions is given.