On a nonlinear Schrödinger system arising in quadratic media

Adán Corcho, Simão Correia, Filipe Oliveira +1

We consider the quadratic Schrödinger system $$i{u}_t+{\Delta }_{{\gamma }_1}u+\overline{u}v=0$$ $$2i{v}_t+{\Delta }_{{\gamma }_2}v-\beta v+\frac{1}{2}{u}^2=0,$$ where $t\in \mathbf{R},x\in {\mathbf{R}}^d\times \mathbf{R}$, in…