Solitary vortex carrying capillary-gravity waves
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We prove the existence of solitary wave solutions to the incompressible, irrotational Euler equations carrying a point or hollow vortex in finite depth. Our analysis treats waves influenced by both gravity and surface tension, i.e. capillary-gravity waves. The second section of the paper is dedicated the formulation of the problem for a wave-borne point vortex, followed by the proof of existence of solutions. Moreover, we provide the leading order terms of the asymptotic form of these solutions. Finally, the hollow vortex problem is treated in the third section; this is achieved by using vortex disingularization. Our techniques specifically address fast moving waves with O(1) vortex strength.
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M.S.