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Particle trajectories in solitary water waves. (English) Zbl 1126.76012
The primary aim is to describe the particle trajectories in the fluid as a solitary wave propagates on the water free surface. Analysing the free boundary problem for harmonic functions in an infinite plane domain, the authors prove that in a solitary wave each particle is transported in the wave direction slower than the wave speed. As the solitary wave propagates, all particles located ahead of the wave crets are lifted, while those behind it experience a downward motion, with the particle trajectory having asymptotically the same height above the flat bed. The authors also comment on related problems within water wave theory comparing with the particle motion in periodic steady water waves.
Reviewer: Argiris I. Delis
MSC:
76B25Solitary waves (inviscid fluids)
35Q51Soliton-like equations