A numerical dressing method for the nonlinear superposition of solutions of the KdV equation

被引：13

作者：

Trogdon, Thomas ^{[1
]}

Deconinck, Bernard ^{[2
]}

机构：

[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[2] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA

来源：

NONLINEARITY | 2014年 / 27卷 / 01期

基金：

美国国家科学基金会;

关键词：

Riemann-Hilbert problems; Korteweg-de Vries equation; finite-genus solutions; Riemann surfaces; numerical analysis; RIEMANN-HILBERT PROBLEMS; STEEPEST DESCENT METHOD;

D O I：

10.1088/0951-7715/27/1/67

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg-de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t.

引用

页码：67 / 86

页数：20

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