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VOLUME 59 (1994) | ISSUE 9 | PAGE 593
New type of solitary gravity wave at the surface of a deep liquid
A new nonlinear integrodifferential equation describing gravity waves at the free surface of an ideal liquid of infinite depth is constructed in 2D hydrodynamics. Exact solitary-wave solutions of this equation are derived. The velocity field in these solutions is a strongly nonmonotonic function of the distance from the surface. The potential flow associated with such a wave contains moving local vortex singularities, both inside and outside the liquid. For irrotational flows, a generalization is made to the case of a liquid of finite depth.