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A new equation describing travelling water waves

Published online by Cambridge University Press:  01 February 2013

Katie Oliveras*
Mathematics Department, Seattle University, Seattle, WA 98122-1090, USA
Vishal Vasan
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
Email address for correspondence:


A new single equation for the surface elevation of a travelling water wave in an incompressible, inviscid, irrotational fluid is derived. This new equation is derived without approximation from Euler’s equations, valid for both a one- and two-dimensional travelling-wave surface. We show that this new formulation can be used to efficiently derive higher-order Stokes-wave approximations, and pose that this new formulation provides a useful framework for further investigation of travelling water waves.

©2013 Cambridge University Press

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