Simão Correia — Page 3

arXiv2015

Stability of ground-states for a system of $M$ coupled semilinear Schrödinger equations

We focus on the study of the stability properties of ground-states for the system of $M$ coupled semilinear Schrödinger equations with power-type nonlinearities and couplings. Our results are generalizations of the theory for the single equation and the technique for this kind of results is simplified. Depending on the power of the nonlinearity, we may observe stability, instability and weak instability. We also obtain results for three distinct classes of bound-states, which is a special feature of the $M\ge2$ case.

math.AP↗

arXiv2014

Blowup for the nonlinear Schrödinger equation with an inhomogeneous damping term in the $L^2$ critical case

We consider the nonlinear Schrödinger equation with $L^2$-critical exponent and an inhomogeneous damping term. By using the tools developed by Merle and Raphael, we prove the existence of blowup phenomena in the energy space $H^1(\mathbb{R})$.

math.AP↗