Wilton Ripples in Weakly Nonlinear Models of Water Waves: Existence and Computation

Autor:	Benjamin F. Akers, David P. Nicholls
Rok vydání:	2021
Předmět:	Partial differential equation Applied Mathematics Computation Numerical analysis Mathematical analysis Harmonic (mathematics) Fixed point Computational Mathematics Nonlinear system Fixed-point iteration Modeling and Simulation Arch Analysis Mathematics
Zdroj:	Water Waves. 3:491-511
ISSN:	2523-3688 2523-367X
DOI:	10.1007/s42286-021-00052-2
Popis:	In this contribution, we prove that small amplitude, resonant harmonic, spatially periodic traveling waves (Wilton ripples) exist in a family of weakly nonlinear PDEs which model water waves. The proof is inspired by that of Reeder and Shinbrot (Arch. Rat. Mech. Anal. 77:321–347, 1981) and complements the authors’ recent, independent result proven by a perturbative technique (Akers and Nicholls 2021). The method is based on a Banach Fixed Point Iteration and, in addition to proving that this iteration has Wilton ripples as a fixed point, we use it as a numerical method for simulating these solutions. The output of this numerical scheme and its performance are evaluated against a quasi-Newton iteration.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7207c5fec7777aefbd4801e40d8ce67b https://doi.org/10.1007/s42286-021-00052-2 Zobrazit plný text záznamu Full text from SpringerLink