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Scattering operator for semirelativistic Hartree type equation with a short range potential. (English) Zbl 1374.35330
Based on the authors’ abstract: In this paper, the authors showed the existence of the scattering operator in the neighborhood of the origin in $$H^{\omega ,1}\cap H^{\mu}$$, where $$\mu >\omega =1+\frac2n$$ for the semirelativistic Hartree type equation $i\partial_tu=\sqrt{M^2-\Delta}u+F(u),\quad (t,x)\in\mathbb{R}\times\mathbb{R}^n,$ where $$F(u)=(|x|^{-\gamma} \ast |u|^2)u$$, $$1<\gamma <2$$, $$n\geq 3$$ and $$\ast$$ denotes the convolution.

##### MSC:
 35Q40 PDEs in connection with quantum mechanics 35Q55 NLS equations (nonlinear Schrödinger equations) 47J35 Nonlinear evolution equations