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arXiv · 1604.01092

Integral and asymptotic properties of solitary waves in deep water

Miles H. Wheeler
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Abstract

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 a related integral identity which rules out waves of pure elevation or pure depression.

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Miles H. Wheeler. 2016-04-04. Integral and asymptotic properties of solitary waves in deep water. https://doi.org/10.1002/cpa.21786

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