作为巴边科方程解的峰值斯托克斯波

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-11-04 DOI:10.1016/j.aml.2024.109359

Spencer Locke, Dmitry E. Pelinovsky

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引用次数: 0

摘要

巴边科方程描述了全形坐标中的水波。过去，人们曾用它来分析和数值求得具有平滑剖面的斯托克斯波的特性。我们在深水极限中证明，具有峰状剖面的斯托克斯波的特性也可以从相同的巴本科方程中得到。为了对奇点进行局部分析，我们将 Babenko 方程重写为最大海拔附近的定点问题。作为副产品，我们的结果排除了全形坐标中的角点奇异性，而该奇异性是在巴本科方程的局部版本中得到的。

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Peaked Stokes waves as solutions of Babenko’s equation

Babenko’s equation describes traveling water waves in holomorphic coordinates. It has been used in the past to obtain properties of Stokes waves with smooth profiles analytically and numerically. We show in the deep-water limit that properties of Stokes waves with peaked profiles can also be recovered from the same Babenko’s equation. In order to develop the local analysis of singularities, we rewrite Babenko’s equation as a fixed-point problem near the maximal elevation level. As a by-product, our results rule out a corner point singularity in the holomorphic coordinates, which has been obtained in a local version of Babenko’s equation.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.