We recall some features of the focusing cubic Schrodinger equation in space dimension 1, 2, and 3. We then see how the introduction of a quintic defocusing term, motivated by physics, modifies the properties of the equation: Cauchy problem, dispersive behavior (in 2D), and solitary waves. In passing, we show that two different notions of stability of solitary waves are commonly used: although they coincide in the case of homogeneous nonlinearites, the cubic-quintic case shows that they may differ. We also list some open questions. The talk is based on a joint work with Christof Sparber.
Online on zoom: https://us02web.zoom.us/j/83520111787