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On the pressure transfer function for solitary water waves with vorticity

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Abstract

In this paper we analyse the role which the pressure function on the sea-bed plays in determining solitary waves with vorticity. We prove that the pressure function on the flat bed determines a unique, real analytic solitary wave solution to the governing equations, given a real analytic vorticity distribution. In particular, the pressure function on the flat bed prescribes a unique surface profile for the resulting solitary water wave.

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Acknowledgments

The author would like to thank the anonymous referee for useful suggestions.

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  1. School of Mathematical Sciences, University College Cork, Cork, Ireland

    David Henry

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  1. David Henry
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Correspondence to David Henry.

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Henry, D. On the pressure transfer function for solitary water waves with vorticity. Math. Ann. 357, 23–30 (2013). https://doi.org/10.1007/s00208-013-0899-0

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  • DOI: https://doi.org/10.1007/s00208-013-0899-0

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