The Effects of Finite Depth on the Propagation of Nonlinear Wave Packets

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Abstract
It is shown that soliton wave packets have some unexpected properties when they move on waters of finite depth and, in particular, that the wave packet forces a long gravity wave. Furthermore, the long gravity wave affects the shape of the wave packet in factors that decay linearly with increasing depth. Thus, although the carrier wave may be effectively short compared with the depth, the wave packet is not. Abstract It is shown that soliton wave packets have some unexpected properties when they move on waters of finite depth and, in particular, that the wave packet forces a long gravity wave. Furthermore, the long gravity wave affects the shape of the wave packet in factors that decay linearly with increasing depth. Thus, although the carrier wave may be effectively short compared with the depth, the wave packet is not.

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