Integral and asymptotic properties of solitary waves in deep water
arXiv:1604.01092 · doi:10.1002/cpa.21786
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.
11 pages
References in corpus (5)
- A variational reduction and the existence of a fully-localised solitary wave for the three-dimensional water-wave problem with weak surface tension
- Global solutions of the gravity-capillary water-wave system in three dimensions
- On 3D water waves system above a flat bottom
- Global solution for the 3D gravity water waves system above a flat bottom
- Kinetic, potential and surface tension energies of solitary waves in deep water