With technological advances in nonlinear optics, it is possible to engineer properties in the propagating medium including linear dispersion. This seminar presents analytical and numerical studies of the Nonlinear Schroedinger equation (NLSE) model, where the usual second order dispersion is replaced by a fourth order one. Results will be presented both in a conservative (Hamiltonian) and non-conservative framework, highlighting interesting properties that depart from the integrable NLSE.