ANALYTICAL INVESTIGATION OF THE CAUDREY-DODD-GIBBON-KOTERA-SAWADA EQUATION USING SYMBOLIC COMPUTATION

被引：4

作者：

Xu, Xiao-Ge ^{[1
,2
]}

Meng, Xiang-Hua ^{[1
]}

Zhang, Chun-Yi ^{[3
,4
]}

Gao, Yi-Tian ^{[3
,4
,5
]}

机构：

[1] Beijing Informat Sci & Technol Univ, Beijing 100192, Peoples R China

[2] Beijing Univ Aeronaut & Astronaut, Sch Sci, Beijing 100083, Peoples R China

[3] Beijing Univ Aeronaut & Astronaut, Minist Educ, Key Lab Fluid Mech, Beijing 100083, Peoples R China

[4] Beijing Univ Aeronaut & Astronaut, Natl Lab Computat Fluid Dynam, Beijing 100083, Peoples R China

[5] Beijing Univ Aeronaut & Astronaut, State Key Lab Software Dev Environm, Beijing 100083, Peoples R China

来源：

INTERNATIONAL JOURNAL OF MODERN PHYSICS B | 2013年 / 27卷 / 06期

基金：

美国国家科学基金会; 中国国家自然科学基金; 北京市自然科学基金;

关键词：

Hirota bilinear method; CDGKS equation; soliton solutions; Lax pair; nonlinear superposition formula; symbolic computation; NONLINEAR SCHRODINGER MODEL; DE-VRIES EQUATION; BACKLUND TRANSFORMATION; KDV EQUATION; DIFFERENTIAL-EQUATIONS; MULTISOLITON SOLUTION; SOLITON-SOLUTIONS; OPTICAL-FIBERS; DUSTY PLASMA; REDUCTIONS;

D O I：

10.1142/S021797921250124X

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

In this paper, the Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation is analytically investigated using the Hirota bilinear method. Based on the bilinear form of the CDGKS equation, its N-soliton solution in explicit form is derived with the aid of symbolic computation. Besides the soliton solutions, several integrable properties such as the Backlund transformation, the Lax pair and the nonlinear superposition formula are also derived for the CDGKS equation.

引用

页数：11

共 47 条

[1] Symbolic calculation in chemistry: Selected examples [J].

Barnett, MP ;

Capitani, JF ;

von zur Gathen, J ;

Gerhard, J .

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, 2004, 100 (02) :80-104

[2] SIMILARITY REDUCTIONS FROM EXTENDED PAINLEVE EXPANSIONS FOR NONINTEGRABLE EVOLUTION-EQUATIONS [J].

CARIELLO, F ;

TABOR, M .

PHYSICA D, 1991, 53 (01) :59-70

[3] NEW HIERARCHY OF KORTEWEG-DEVRIES EQUATIONS [J].

CAUDREY, PJ ;

DODD, RK ;

GIBBON, JD .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1976, 351 (1666) :407-422

[4] CONSTRAINTS OF THE 2+1 DIMENSIONAL INTEGRABLE SOLITON SYSTEMS [J].

CHENG, Y ;

LI, YS .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1992, 25 (02) :419-431

[5] Response to "Comment on 'A new mathematical approach for finding the solitary waves in dusty plasma'" [Phys. Plasmas 6, 4392 (1999)] [J].

Das, GC ;

Sarma, J .

PHYSICS OF PLASMAS, 1999, 6 (11) :4394-4397

[6] A bidirectional Kaup-Kupershmidt equation and directionally dependent solitons [J].

Dye, JM ;

Parker, A .

JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (10) :4921-4949

[7]

Eisenhart Luther Pfahler, 1960, TREATISE DIFFERENTIA

[8] Extended tanh-function method and its applications to nonlinear equations [J].

Fan, EG .

PHYSICS LETTERS A, 2000, 277 (4-5) :212-218

[9] THE BI-HAMILTONIAN STRUCTURE OF SOME NON-LINEAR 5TH-ORDER AND 7TH-ORDER DIFFERENTIAL-EQUATIONS AND RECURSION FORMULAS FOR THEIR SYMMETRIES AND CONSERVED COVARIANTS [J].

FUCHSSTEINER, B ;

OEVEL, W .

JOURNAL OF MATHEMATICAL PHYSICS, 1982, 23 (03) :358-363

[10] On the non-planar dust-ion-acoustic waves in cosmic dusty plasmas with transverse perturbations [J].

Gao, Yi-Tian ;

Tian, Bo .

EPL, 2007, 77 (01)

← 1 2 3 4 5 →