Integral and Asymptotic Properties of Solitary Waves in Deep Water

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We consider two- and three-dimensional gravity and gravity-capillary solitary water waves in infinite depth. Assuming algebraic decay rates for the free surface and velocity potential, we show that the velocity potential necessarily behaves like a dipole at infinity and obtain a related asymptotic formula for the free surface. We then prove an identity relating the “dipole moment” to the kinetic energy. This implies that the leading-order terms in the asymptotics are nonvanishing and in particular that the angular momentum is infinite. Lastly we prove that the “excess mass” vanishes.

Original languageEnglish
Pages (from-to)1941-1956
Number of pages16
JournalCommunications on Pure and Applied Mathematics
Issue number10
Publication statusE-pub ahead of print - 16 Aug 2018

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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