Analytical Approximation for 2-D Nonlinear Periodic Deep Water Waves

TL;DR

This paper extends a recent method to analytically approximate 2D steady water waves with rigorous error bounds, applicable to non-small wave heights, revealing analytic wave shapes in a nonlocal equation context.

Contribution

It introduces a general analytical approximation method for 2D nonlinear steady water waves with error bounds, applicable beyond small wave steepness.

Findings

Wave shapes are shown to be analytic.

The method provides rigorous error bounds.

Applicable to heights near the critical, not just small amplitudes.

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.