Auto-Backlund transformation and similarity reductions for general variable coefficient KdV equations

被引：138

作者：

Fan, EG ^{[1
]}

机构：

[1] Fudan Univ, Inst Math, Shanghai 200433, Peoples R China

来源：

PHYSICS LETTERS A | 2002年 / 294卷 / 01期

基金：

中国博士后科学基金;

关键词：

homogeneous balance method; general variable coefficient KdV equation Backlund transformation; Lax pairs; symmetry; analytic solution; similarity reduction;

D O I：

10.1016/S0375-9601(02)00033-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Based on the idea of the homogeneous balance (HB) method. we study the Backlund transformation and similarity reductions of general variable coefficient KdV equation. It is found that the corresponding results are coincide with those by Weiss-Tabor-Carnevale (WTC) method and Clarkson-Kruskal (CK) method. respectively. The close connections among the HB, WTC and CK methods are exposured in theory. In the meantime, a Lax pair. a symmetry. two conservation laws and a analytic solution for the general variable coefficient KdV equation are given. (C) 2002 Elsevier Science B.V. All rights reserved.

引用

页码：26 / 30

页数：5

共 17 条

[1]

ALINI JN, 1987, PHYS LETT A, V125, P456

[2]

[Anonymous], 1986, APPL LIE GROUP DIFFE, DOI DOI 10.1007/978-1-4684-0274-2

[3]

BLUMAN GM, 1974, SIMILARITY METHODS

[4] PAINLEVE PROPERTY, AUTO-BACKLUND TRANSFORMATION, LAX PAIRS, AND REDUCTION TO THE STANDARD FORM FOR THE KORTEWEG-DEVRIES EQUATION WITH NONUNIFORMITIES [J].

BRUGARINO, T .

JOURNAL OF MATHEMATICAL PHYSICS, 1989, 30 (05) :1013-1015

[5]

CHAN ML, 1989, J MATH PHYS, V30, P359

[6] NEW SIMILARITY SOLUTIONS FOR THE MODIFIED BOUSSINESQ EQUATION [J].

CLARKSON, PA .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1989, 22 (13) :2355-2367

[7] NEW SIMILARITY REDUCTIONS OF THE BOUSSINESQ EQUATION [J].

CLARKSON, PA ;

KRUSKAL, MD .

JOURNAL OF MATHEMATICAL PHYSICS, 1989, 30 (10) :2201-2213

[8] Two new applications of the homogeneous balance method [J].

Fan, EG .

PHYSICS LETTERS A, 2000, 265 (5-6) :353-357

[9] SLOWLY VARYING SOLITARY WAVES .1. KORTEWEG-DE-VRIES EQUATION [J].

GRIMSHAW, R .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1979, 368 (1734) :359-375

[10] Auto-Backlund transformation and analytic solutions for general variable-coefficient KdV equation [J].

Hong, WY ;

Jung, YD .

PHYSICS LETTERS A, 1999, 257 (3-4) :149-152

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