Exact solutions to a nonlinearly dispersive Schrödinger equation

By using the theory of dynamical systems to a nonlinearly dispersive Schrödinger equation, the existence of solitary patterns, compactons, smooth and non-smooth periodic patterns and breather solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee existence of the above solutions are given. In some simple conditions, exact explicit and implicit parametric representations of solutions are given.