New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation

被引：6

作者：

Polat, Gulden Gun ^{[1
]}

Ozer, Teoman ^{[2
]}

机构：

[1] Istanbul Tech Univ, Dept Math, Fac Sci & Letters, TR-34469 Istanbul, Turkey

[2] Istanbul Tech Univ, Fac Civil Engn, Div Mech, TR-34469 Istanbul, Turkey

来源：

JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS | 2017年 / 12卷 / 04期

关键词：

Jacobi last multipliers; Lagrangians; lambda-symmetries; first integrals; modified Emden equation; Prelle-Singer method; INTEGRABILITY; SYMMETRIES; SYSTEMS; JACOBI;

D O I：

10.1115/1.4035408

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

This study deals with the determination of Lagrangians, first integrals, and integrating factors of the modified Emden equation by using Jacobi and Prelle-Singer methods based on the Lie symmetries and lambda-symmetries. It is shown that the Jacobi method enables us to obtain Jacobi last multipliers by means of the Lie symmetries of the equation. Additionally, via the Lie symmetries of modified Emden equation, we analyze some mathematical connections between lambda-symmetries and Prelle-Singer method. New and nontrivial Lagrangian forms, conservation laws, and exact solutions of the equation are presented and discussed.

引用

页数：15

共 42 条

[11] SOLUTIONS OF A GENERALIZED EMDEN EQUATION AND THEIR PHYSICAL SIGNIFICANCE [J].

DIXON, JM ;

TUSZYNSKI, JA .

PHYSICAL REVIEW A, 1990, 41 (08) :4166-4173

[12] ONE-DIMENSIONAL EQUATIONS WITH THE MAXIMUM NUMBER OF SYMMETRY GENERATORS [J].

DUARTE, LGS ;

DUARTE, SES ;

MOREIRA, IC .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1987, 20 (11) :L701-L704

[13]

Erwin V. J., 1984, WAVE PHENOMENON MODE

[14]

Golubev V. V., 1950, LECT ANAL THEORY DIF

[15] Comment on 'On the general solution for the modified Emden-type equation x+αxx+βx3=0' [J].

Iacono, R. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (06)

[16]

Ibragimov N.H., 1994, symmetries, exact solutions and conservation laws, V1-2

[17]

Jacobi C G J., 1845, J. Reine Angew. Math, V29, P213

[18]

Jacobi C.G.J., 1844, GIORNALE ARCADICO SC, VXCIX, P129

[19]

JACOBI CGJ, 1844, J REINE ANGEW MATH, V27, P199, DOI DOI 10.1515/CRLL.1844.27.199

[20] 1ST INTEGRALS FOR THE MODIFIED EMDEN EQUATION Q+ALPHA(T)Q+QN=O [J].

LEACH, PGL .

JOURNAL OF MATHEMATICAL PHYSICS, 1985, 26 (10) :2510-2514

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