Scattering theory for time-dependent Hartree-Fock type equation
This paper concerns the scattering problem for the time-dependent Hartree-Fock type equation \[ i{\partial\over\partial t} u_j= -{1\over 2}\Delta u_j+ f_j(\vec u),\quad (t,x)\in \mathbb{R}\times \mathbb{R}^n\;(n\geq 2), \] \[ u_j(0,x)= \phi_j(x),\quad j= 1,\dots, N, \] where \[ f_j(\vec u)= \sum^N_{k= 1} (V*|u_k|^2) u_j- \sum^N_{k=1} [V*(u_j\overline u_k)] u_k. \] Here \(V(x)=|x|^{-\gamma}\), \(0<\gamma< n\), and \(*\) denotes the convolution in \(\mathbb{R}^n\).
scientific article; zbMATH DE number 1455442