Lie Symmetries, Conservation Laws and Exact Solutions for Two Rod Equations

被引：14

作者：

Liu, Hanze ^{[1
,2
]}

Li, Jibin ^{[1
,3
]}

机构：

[1] Kunming Univ Sci & Technol, Ctr Nonlinear Sci Studies, Kunming 650093, Yunnan, Peoples R China

[2] Binzhou Univ, Dept Math, Binzhou 256603, Shandong, Peoples R China

[3] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

来源：

ACTA APPLICANDAE MATHEMATICAE | 2010年 / 110卷 / 02期

关键词：

Rod equation; Lie symmetry analysis; Conservation law; Similarity reduction; Exact solution;

D O I：

10.1007/s10440-009-9462-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the Lie symmetry analysis are performed for the two rod equations. The infinite number of conservation laws (CLs) for the two equations are derived from the direct method. Furthermore, the all similarity reductions and exact explicit solutions are provided.

引用

页码：573 / 587

页数：15

共 15 条

[1]

[Anonymous], 1993, GRADUATE TEXTS MATH

[2]

Asmar NH, 2005, Partial differential equations with Fourier Series and Boundary Value. Problems, V2nd

[3] New conservation laws obtained directly from symmetry action on a known conservation law [J].

Bluman, George ;

Temuerchaolu ;

Anco, Stephen C. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 322 (01) :233-250

[4]

Cantwell B J., 2002, Introduction to symmetry analysis

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

CLARKSON, PA .

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

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

CLARKSON, PA ;

KRUSKAL, MD .

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

[7] Solitary waves in a quartic nonlinear elastic rod [J].

Duan, WS ;

Zhao, JB .

CHAOS SOLITONS & FRACTALS, 2000, 11 (08) :1265-1267

[8] METHOD FOR SOLVING KORTEWEG-DEVRIES EQUATION [J].

GARDNER, CS ;

GREENE, JM ;

KRUSKAL, MD ;

MIURA, RM .

PHYSICAL REVIEW LETTERS, 1967, 19 (19) :1095-&

[9]

HIROTA R, 1976, SUP PROG THEOR PHYS, P64

[10] Relationship between symmetries and conservation laws [J].

Kara, AH ;

Mahomed, FM .

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2000, 39 (01) :23-40

← 1 2 →