Resonant triads for two bidirectional equations in 1+1 dimensions

被引：8

作者：

Verhoeven, C

机构：

[1] Free Univ Brussels, Theoret Natuurkunde, B-1050 Brussels, Belgium

[2] Free Univ Brussels, Int Solvay Inst Phys & Chem, B-1050 Brussels, Belgium

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2004年 / 37卷 / 44期

关键词：

D O I：

10.1088/0305-4470/37/44/011

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The two-soliton solution of the KdV equation is known not to degenerate into a solution describing resonant triads of, solitons in 1 + 1 dimensions. However, we show that two integrable coupled-KdV systems of the Drinfeld-Sokolov class possess solutions which may degenerate into resonant triads. These solutions are associated with a resonance relation which generalizes the usual one previously considered by Hirota and Ito.

引用

收藏

页码：10625 / 10638

页数：14

相关论文

共 19 条

[1] INTEGRABLE QUARTIC POTENTIALS AND COUPLED KDV EQUATIONS [J].

BAKER, S ;

ENOLSKII, VZ ;

FORDY, AP .

PHYSICS LETTERS A, 1995, 201 (2-3) :167-174

[2] INTEGRABLE MODEL WITH NON-TRIVIAL INTERACTION BETWEEN SUBLUMINAL AND SUPERLUMINAL SOLITONS [J].

BARASHENKOV, IV ;

GETMANOV, BS ;

KOVTUN, VE .

PHYSICS LETTERS A, 1988, 128 (3-4) :182-186

[3] THE UNIFIED APPROACH TO INTEGRABLE RELATIVISTIC-EQUATIONS - SOLITON-SOLUTIONS OVER NONVANISHING BACKGROUNDS .2. [J].

BARASHENKOV, IV ;

GETMANOV, BS .

JOURNAL OF MATHEMATICAL PHYSICS, 1993, 34 (07) :3054-3072

[4] On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy [J].

Biondini, G ;

Kodama, Y .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (42) :10519-10536

[5] The Boussinesq equation revisited [J].

Bogdanov, L ;

Zakharov, VE .

PHYSICA D-NONLINEAR PHENOMENA, 2002, 165 (3-4) :137-162

[6] BREAKING SOLITONS IN 2 + 1-DIMENSIONAL INTEGRABLE EQUATIONS [J].

BOGOYAVLENSKII, OI .

RUSSIAN MATHEMATICAL SURVEYS, 1990, 45 (04) :1-86

[7]

DRINFELD VG, 1981, DOKL AKAD NAUK SSSR+, V258, P11

[8] On bidirectional fifth-order nonlinear evolution equations, Lax pairs, and directionally dependent solitary waves [J].

Dye, JM ;

Parker, A .

JOURNAL OF MATHEMATICAL PHYSICS, 2001, 42 (06) :2567-2589

[9] THE HENON-HEILES SYSTEM REVISITED [J].

FORDY, AP .

PHYSICA D, 1991, 52 (2-3) :204-210

[10] RESONANCE OF SOLITONS IN ONE DIMENSION [J].

HIROTA, R ;

ITO, M .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1983, 52 (03) :744-748