Boundary integral methods for dispersive equations, Airy flow and the modified Korteweg de Vries equation

被引：4

作者：

Franco-de-Leon, Mariano ^{[1
]}

Lowengrub, John ^{[1
]}

机构：

[1] Univ Calif Irvine, 540 H Rowland Hall, Irvine, CA 92697 USA

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2019年 / 45卷 / 01期

关键词：

Dispersive; Solitons; Numerical solution; mKdV; Airy flow; GLOBAL WELL-POSEDNESS; NONLINEAR EVOLUTION; STABILITY ANALYSIS; DEVRIES EQUATION; KDV; CONVERGENCE;

D O I：

10.1007/s10444-018-9607-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we implement interface tracking methods for the evolution of 2-D curves that follow Airy flow, a curvature-dependent dispersive geometric evolution law. The curvature of the curve satisfies the modified Korteweg de Vries equation, a dispersive non-linear soliton equation. We present a fully discrete space-time analysis of the equations (proof of convergence) and numerical evidence that confirms the accuracy, convergence, efficiency, and stability of the methods.

引用

页码：99 / 135

页数：37

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