Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent

被引：140

作者：

Grunert, Katrin ^{[1
]}

Teschl, Gerald ^{[1
,2
]}

机构：

[1] Univ Vienna, Fac Math, A-1090 Vienna, Austria

[2] Int Erwin Schrodinger Inst Math Phys, A-1090 Vienna, Austria

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2009年 / 12卷 / 03期

基金：

奥地利科学基金会;

关键词：

Riemann-Hilbert problem; KdV equation; Solitons; INVERSE SCATTERING; TODA LATTICE; BEHAVIOR;

D O I：

10.1007/s11040-009-9062-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg-de Vries equation for decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction to this method.

引用

页码：287 / 324

页数：38

共 40 条

[1]

ABLOWITZ MJ, 1977, STUD APPL MATH, V57, P13

[2]

DECAY OF CONTINUOUS SPECTRUM FOR SOLUTIONS OF KORTEWEG-DEVRIES EQUATION [J].

ABLOWITZ, MJ ;

NEWELL, AC .

JOURNAL OF MATHEMATICAL PHYSICS, 1973, 14 (09) :1277-1284

[3]

[Anonymous], ZH EKSP TEOR FIZ

[4]

[Anonymous], 1975, PUBL RES I MATH SCI, DOI DOI 10.2977/PRIMS/1195192000

[5]

[Anonymous], 1982, Soviet Math. Dokl.

[6]

[Anonymous], 1972, PUBL RES I MATH SCI, DOI DOI 10.2977/PRIMS/1195192955

[7]

SCATTERING AND INVERSE SCATTERING FOR 1ST ORDER SYSTEMS [J].

BEALS, R ;

COIFMAN, RR .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1984, 37 (01) :39-90

[8]

Beals R.R., 1988, Direct and inverse scattering on the line, V28

[9]

Budylin AM, 1996, DOKL AKAD NAUK+, V348, P455

[10]

BUSLAEV VS, 1986, J SOVIET MATH, V34, P1905, DOI DOI 10.1007/bf01095099

← 1 2 3 4 →