  The linearization of the classical Boussinesq system is solved explicitly in
the case of nonzero boundary conditions on the half-line. The analysis relies
on the unified transform method of Fokas and is performed in two different
frameworks: (i) by exploiting the recently introduced extension of Fokas's
method to systems of equations; (ii) by expressing the linearized classical
Boussinesq system as a single, higher-order equation which is then solved via
the usual version of the unified transform. The resulting formula provides a
novel representation for the solution of the linearized classical Boussinesq
system on the half-line. Moreover, thanks to the uniform convergence at the
boundary, the novel formula is shown to satisfy the linearized classical
Boussinesq system as well as the prescribed initial and boundary data via a
direct calculation.
