Analytical Approximation for 2-D Nonlinear Periodic Deep Water Waves

2013/09/20 by S. Tanveer, Tanveer, Saleh
Earth and Planetary Sciences · #76B15 #Arctic and Antarctic ice dynamics #Coastal and Marine Dynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.1309.5801

openalex publication_date 2013/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On Borel summation and Stokes phenomena for rank-1 nonlinear systems of ordinary differential equations
• Analytical approximation of Blasius' similarity solution with rigorous error bounds

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