The Painleve Tests, Backlund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source

被引：1

作者：

Shen, Yali ^{[1
]}

Zhang, Fengqin ^{[1
]}

Feng, Xiaomei ^{[1
]}

机构：

[1] Yuncheng Univ, Dept Math, Yuncheng 044000, Peoples R China

来源：

DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2012年 / 2012卷

关键词：

PARTIAL-DIFFERENTIAL EQUATIONS; SOLITON; HIERARCHY; PROPERTY;

D O I：

10.1155/2012/872385

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Painleve property and Backlund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painleve property. In order to further prove its integrality, we give its bilinear form and construct its bilinear Backlund transformation by the Hirota's bilinear operator. And then the soliton solution of the equation is obtained, based on the proposed bilinear form.

引用

页数：10

共 14 条

[1] EXACT SOLUTION OF KORTEWEG-DE VRIES EQUATION FOR MULTIPLE COLLISIONS OF SOLITONS [J].

HIROTA, R .

PHYSICAL REVIEW LETTERS, 1971, 27 (18) :1192-+

[2]

Hirota R., 2004, CAMBRIDGE TRACTS MAT, V155

[3]

Hone ANW, 2009, LECT NOTES PHYS, V767, P245, DOI 10.1007/978-3-540-88111-7_7

[4] A BACKLUND TRANSFORMATION AND NONLINEAR SUPERPOSITION FORMULA OF A HIGHER-ORDER ITO EQUATION [J].

HU, XB .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1993, 26 (21) :5895-5903

[5] Solving the KdV hierarchy with self-consistent sources by inverse scattering method [J].

Lin, RL ;

Zeng, YB ;

Ma, WX .

PHYSICA A, 2001, 291 (1-4) :287-298

[6]

Ma W.X., APPL MATH L IN PRESS

[7] Soliton, positon and negaton solutions to a Schrodinger self-consistent source equation [J].

Ma, WX .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2003, 72 (12) :3017-3019

[8] NEW FINITE-DIMENSIONAL INTEGRABLE SYSTEMS BY SYMMETRY CONSTRAINT OF THE KDV EQUATIONS [J].

MA, WX .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1995, 64 (04) :1085-1091

[9]

Matsuno Y., 1984, Mathematics in Science and Engineering, V174

[10] THE PAINLEVE PROPERTY FOR PARTIAL-DIFFERENTIAL EQUATIONS [J].

WEISS, J ;

TABOR, M ;

CARNEVALE, G .

JOURNAL OF MATHEMATICAL PHYSICS, 1983, 24 (03) :522-526

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