arXiv subjects

Jorge D. Silva

Publications and source records attributed to Jorge D. Silva.

2 recordsLinked to original sources

arXiv2019

Mass-transfer instability of ground-states for Hamiltonian Schrödinger systems

We study generic semilinear Schrödinger systems which may be written in Hamiltonian form. In the presence of a single gauge invariance, the components of a solution may exchange mass between them while preserving the total mass. We exploit this feature to unravel new orbital instability results for ground-states. More precisely, we first derive a general instability criterion and then apply it to some well-known models arising in several physical contexts. In particular, this mass-transfer instability allows us to exhibit $L^2$-subcritical unstable ground-states.

math.AP↗

arXiv2017

On a nonlinear Schrödinger system arising in quadratic media

We consider the quadratic Schrödinger system $$iu_t+Δ_{γ_1}u+\overline{u}v=0$$ $$2iv_t+Δ_{γ_2}v-βv+\frac 12 u^2=0,$$ where $t\in\mathbf{R},\,x\in \mathbf{R}^d\times \mathbf{R}$, in dimensions $1\leq d\leq 4$ and for $γ_1,γ_2>0$, the so-called elliptic-elliptic case. We show the formation of singularities and blow-up in the $L^2$-(super)critical case. Furthermore, we derive several stability results concerning the ground state solutions of this system.

math.AP↗