Review of well-posedness methods for the 1D nonlinear Schrödinger equation with an application to combined nonlinearities

Alex D. Rodriguez, Gia Azcoitia, Hannah Wubben +1

We consider the nonlinear Schrödinger equation in one dimension with nonlinearities of type $|u{|}^{\alpha }u$ for any power $\alpha >0$ and review two different methods for obtaining solutions, n…