Exact solutions for small-amplitude capillary-gravity water waves

Delia Ionescu-Kruse

Exact solutions for small-amplitude capillary-gravity water waves

Mathematical Physics 2011-06-21 v1 math.MP Fluid Dynamics

Authors: Delia Ionescu-Kruse

Abstract

We present explicit solutions for the ordinary differential equations system describing the motion of the particles beneath small-amplitude capillary-gravity waves which propagate on the surface of an irrotational water flow with a flat bottom. The required computations involve elliptic integrals of first kind, the Legendre normal form and a solvable Abel differential equation of the second kind.

Keywords

partial differential equations

Cite

@article{arxiv.1106.3813,
  title  = {Exact solutions for small-amplitude capillary-gravity water waves},
  author = {Delia Ionescu-Kruse},
  journal= {arXiv preprint arXiv:1106.3813},
  year   = {2011}
}