Physics – Mathematical Physics
Scientific paper
2011-06-20
Wave Motion 46 (2009), 379--388
Physics
Mathematical Physics
Scientific paper
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.
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