Radiation of solitons by slender bodies advancing in a shallow channel

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Abstract
It is known from recent experiments that the disturbance due to a slender ship advancing in a shallow channel is essentially one-dimensional in the horizontal plane. In particular solitons can be radiated upstream in a transient manner. In this note we develop a theory for soliton radiation by slender bodies. It is shown that, when the ship speed is in the transcritical range, one-dimensional upstream influence can occur even when the channel width is nearly of the order of the ship length but much greater than the ship beam. The theory is also extended to one or more ships travelling in the same channel at near-critical speeds.