We consider the following nonlinear Schr\"{o}dinger equation of derivative type: \begin{equation}i \partial_t u + \partial_x^2 +i |u|^{2} \partial_x +b|u|^4u=0 , \quad (t,x) \in \mathbb{R}\times\mathbb{R}, \ b \in\mathbb{R}. \end{equation} If $b=0$, this is known as a gauge equivalent form well-known (DNLS), which mass critical and completely integrable. The can be considered generalized DNLS w...

In this paper, we investigate the initial boundary value problem for a fourth order wave equation with Newtonian potential. We establish firstly local existence of solutions by Banach fixed point theorem. Using potential well argument, show global existence, finite time blow-up, asymptotic behavior since energy is not over depth well. Finally, when supercritical, give some explicit criterion bl...