Inverse scattering transform, KdV, and solitons

被引：0

作者：

Aktosun, T ^{[1
]}

机构：

[1] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

来源：

CURRENT TRENDS IN OPERATOR THEORY AND ITS APPLICATIONS | 2004年 / 149卷

关键词：

Korteweg-de Vries equation; inverse scattering transform; soliton;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this review paper, the Korteweg-de Vries equation (KdV) is considered, and it is derived by using the Lax method and the AKNS method. An outline of the inverse scattering problem and of its solution is presented for the associated Schrodinger equation on the line. The inverse scattering transform is described in order to solve the initial-value problem for the KdV, and the time evolution of the corresponding scattering data is obtained. Soliton solutions to the KdV are derived in several ways.

引用

页码：1 / 22

页数：22

共 26 条

[1]

Ablowitz M.J., 1991, SOLITONS NONLINEAR E

[2] METHOD FOR SOLVING SINE-GORDON EQUATION [J].

ABLOWITZ, MJ ;

KAUP, DJ ;

NEWELL, AC ;

SEGUR, H .

PHYSICAL REVIEW LETTERS, 1973, 30 (25) :1262-1264

[3]

Ablowitz MJ., 1981, SOLITONS INVERSE SCA, V4

[4] Small-energy asymptotics for the Schrodinger equation on the line [J].

Aktosun, T ;

Klaus, M .

INVERSE PROBLEMS, 2001, 17 (04) :619-632

[5]

Aktosun T, 2001, SCATTERING, P770

[6]

[Anonymous], 1989, INVERSE PROBLEMS QUA

[7] INVERSE SCATTERING ON THE LINE [J].

DEIFT, P ;

TRUBOWITZ, E .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1979, 32 (02) :121-251

[8]

DRAZIN PG, 1986, SOLITONS

[9]

Faddeev L D., 1967, Amer. Math. Soc., Transl., II Ser., V65, P139

[10]

Fermi E., 1955, LECT APPL MATH

← 1 2 3 →