The author considers the abstract wave equation \(u_{tt}=-Lu\), where \(L\) is such a self-adjoint operator on a Hilbert space that \(L\) is an extension of the square \(B^2\) of a simple maximal symmetric operator \(B\), and \((Lu,u)=\|B^*u\|^2\) for any \(u\in D(L)\).
Under these assumptions an analogue of the Lax-Phillips scattering scheme is developed. In particular, the structure of the incoming and outgoing subspaces is described. The translation representation of the corresponding group of operators is obtained.