This paper concerns homoclinic solutions to periodic orbits in a fourth-order Hamiltonian system arising from a reduction of the classical water-wave problem in the presence of surface tension. These solutions correspond to travelling solitary waves which converge to non-decaying ripples at innnity. An analytical result of Amick and Toland, showing the existence of such homoclinic orbits to sma...

We consider the Dirac operator on asymptotically static Lorentzian manifolds with an odd-dimensional compact Cauchy surface. prove that if Atiyah-Patodi-Singer boundary conditions are imposed at infinite times then is Fredholm. This generalizes a theorem due to B\"ar-Strohmaier in case of finite times, and we also show corresponding index formula extends setting. Furthermore, demonstrate existe...