Forced gravity-capillary solitary waves

This Note is devoted to the propagation of capillary-gravity waves forced by a pressure distribution acting focally on the free surface and moving at a constant velocity. The analysis is performed near the minimum velocity of the dispersion curve. Near this velocity, the linearized theory developed by Rayleigh [9] is no longer valid and one must include nonlinear terms. In order to do this, we use the theory developed by Mielke [7] for the forced propagation of gravity waves near critical Froude number (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.