Analytical Approximation for 2-D Nonlinear Periodic Deep Water Waves

Abstract

A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for a set of parameter values that correspond to heights slightly smaller than the critical. The wave shapes are shown to be analytic. The method presented in quite general and does not assume smallness of wave height or steepness and can be readily extended to other interfacial problems involving Laplace's equation.

33 pages

References in corpus (2)

• Proof of the Dubrovin conjecture and analysis of the tritronquée solutions of $P_I$
• Analytical approximation of Blasius' similarity solution with rigorous error bounds