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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
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