ﻻ يوجد ملخص باللغة العربية
We consider the quadratic Schrodinger system $$iu_t+Delta_{gamma_1}u+overline{u}v=0$$ $$2iv_t+Delta_{gamma_2}v-beta v+frac 12 u^2=0,$$ where $tinmathbf{R},,xin mathbf{R}^dtimes mathbf{R}$, in dimensions $1leq dleq 4$ and for $gamma_1,gamma_2>0$, 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.
In this paper, we study the solutions to the energy-critical quadratic nonlinear Schrodinger system in ${dot H}^1times{dot H}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${rm u}_0$ is radial or non-r
We study the nonlinear Schrodinger system [ begin{cases} displaystyle iu_t+Delta u-u+(frac{1}{9}|u|^2+2|w|^2)u+frac{1}{3}overline{u}^2w=0, idisplaystyle sigma w_t+Delta w-mu w+(9|w|^2+2|u|^2)w+frac{1}{9}u^3=0, end{cases} ] for $(x,t)in mathbb{R
In this paper, we simplify the proof of M. Hamano in cite{Hamano2018}, scattering theory of the solution to eqref{NLS system}, by using the method from B. Dodson and J. Murphy in cite{Dodson2018}. Firstly, we establish a criterion to ensure the solut
We study the existence of ground states for the coupled Schrodinger system begin{equation} left{begin{array}{lll} displaystyle -Delta u_i+lambda_i u_i= mu_i |u_i|^{2q-2}u_i+sum_{j eq i}b_{ij} |u_j|^q|u_i|^{q-2}u_i u_iin H^1(mathbb{R}^n), quad i=1,
We study an elliptic equation with measurable coefficients arising from photo-acoustic imaging in inhomogeneous media. We establish Holder continuity of weak solutions and obtain pointwise bounds for Greens functions subject to Dirichlet or Neumann condition.