Dynamics of blow-up solutions for the Schrödinger–Choquard equation

oleh: Cunqin Shi, Kun Liu

Format: Article
Diterbitkan: SpringerOpen 2018-04-01

Deskripsi

Abstract In this paper, we study the dynamics of blow-up solutions for the nonlinear Schrödinger–Choquard equation iψt+Δψ=λ1|ψ|p1ψ+λ2(Iα∗|ψ|p2)|ψ|p2−2ψ. $$i\psi_{t}+\Delta \psi =\lambda_{1}\vert \psi \vert ^{p_{1}}\psi +\lambda_{2}\bigl(I _{\alpha }\ast \vert \psi \vert ^{p_{2}}\bigr)\vert \psi \vert ^{p_{2}-2}\psi. $$ We first show existence of blow-up solutions and obtain a sharp threshold mass of global existence and blow-up for this equation with λ1>0 $\lambda_{1}>0$, λ2<0 $\lambda_{2}<0$, 0<p1<4N $0< p_{1}<\frac{4}{N}$ and p2=1+2+αN $p_{2}=1+\frac{2+\alpha }{N}$. Then we obtain some dynamical properties of blow-up solutions by the corresponding ground state of this equation with λ1=0 $\lambda_{1}=0$.