Title: Scattering in the energy space for Boussinesq equations,
Abstract: In this note we show that all small solutions in the energy space of the
generalized 1D Boussinesq equation must decay to zero as time tends to
infinity, strongly on slightly proper subsets of the space-time light cone. Our
result does not require any assumption on the power of the nonlinearity,
working even for the supercritical range of scattering. No parity assumption on
the initial data is needed.