Exact Solitary Water Waves with Vorticity |
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Authors: | Vera Mikyoung Hur |
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Institution: | (1) Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA |
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Abstract: | The solitary water wave problem is to find steady free surface waves which approach a constant level of depth in the far field.
The main result is the existence of a family of exact solitary waves of small amplitude for an arbitrary vorticity. Each solution
has a supercritical parameter value and decays exponentially at infinity. The proof is based on a generalized implicit function
theorem of the Nash–Moser type. The first approximation to the surface profile is given by the “KdV” equation. With a supercritical
value of the surface tension coefficient, a family of small amplitude solitary waves of depression with subcritical parameter
values is constructed for an arbitrary vorticity. |
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Keywords: | |
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