The linearized classical Boussinesq system on the half‐line

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