Abstract
We show that Gerstner’s wave exhausts all solutions to the gravity water wave problem that have particle paths prescribed by trigonometric polynomials of degree one. We further show that any Ansatz of degree two reduces to Gerstner’s wave.
Acknowledgements
The financial support of the ERC Advanced Grant “Nonlinear studies of water flows with vorticity” is acknowledged. The author would like to thank the referees for several useful comments and suggestions.
Notes
No potential conflict of interest was reported by the author.