Abstract
The method developed by Longuet-Higgins [J. Inst. Math. Appl. 22, 261 (1978)] for the computation of pure gravity waves is extended to capillary-gravity waves in deep water. Surface tension provides an additional term in the identities between the Fourier coefficients in Stokes’ expansion. This term is then reduced to a simple function of the slope of the local tangent to the profile of the free surface. A set of nonlinear algebraic equations is derived and solved by using the Newton’s method. A new family of limiting profiles of steady gravity waves with surface tension is found.
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