Coupled Higgs field equation and Hamiltonian amplitude equation: Lie classical approach and (G′/G)-expansion method

被引：106

作者：

Kumar, Sachin ^{[1
]}

Singh, K. ^{[2
]}

Gupta, R. K. ^{[1
]}

机构：

[1] Thapar Univ, Sch Math & Comp Applicat, Patiala 147004, Punjab, India

[2] Jaypee Univ Informat Technol, Dept Math, Waknaghat 173234, India

来源：

PRAMANA-JOURNAL OF PHYSICS | 2012年 / 79卷 / 01期

关键词：

Lie classical method; the (G '/G)-expansion method; travelling wave solutions; coupled Higgs equation; Hamiltonian amplitude equation; ELLIPTIC FUNCTION SOLUTIONS; WAVE SOLUTIONS; NONLINEAR EVOLUTION; TANH METHOD; FAMILIES;

D O I：

10.1007/s12043-012-0284-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (G'/G)-expansion method, where G = G(xi) satisfies a second-order linear ordinary differential equation (ODE). The travelling wave solutions expressed by hyperbolic, trigonometric and the rational functions are obtained.

引用

页码：41 / 60

页数：20

共 19 条

[1] The extended tanh method and its applications for solving nonlinear physical models
Abdou, M. A.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (01) : 988 - 996
[2] Similarity: generalizations, applications and open problems
Bluman, G.
Broadbridge, P.
King, J. R.
Ward, M. J.
[J]. JOURNAL OF ENGINEERING MATHEMATICS, 2010, 66 (1-3) : 1 - 9
[3] Bluman G. W., 2013, Symmetries and Differential Equations, V81
[4] Symmetry analysis and some exact solutions of cylindrically symmetric null fields in general relativity
Gupta, R. K.
Singh, K.
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (11) : 4189 - 4196
[5] SOME EXACT RESULTS FOR NONLINEAR DIFFUSION WITH ABSORPTION
HILL, JM
AVAGLIANO, AJ
EDWARDS, MP
[J]. IMA JOURNAL OF APPLIED MATHEMATICS, 1992, 48 (03) : 283 - 304
[6] Jacobi elliptic function solutions for two variant Boussinesq equations
Lü, D
[J]. CHAOS SOLITONS & FRACTALS, 2005, 24 (05) : 1373 - 1385
[7] The tanh method .1. Exact solutions of nonlinear evolution and wave equations
Malfliet, W
Hereman, W
[J]. PHYSICA SCRIPTA, 1996, 54 (06): : 563 - 568
[8] Olver PJ., 2000, Applications of Lie Groups to Differential Equations
[9] Benjamin-Bona-Mahony (BBM) equation with variable coefficients: Similarity reductions and Painleve analysis
Singh, K.
Gupta, R. K.
Kumar, Sachin
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (16) : 7021 - 7027
[10] ON N-SOLITON SOLUTIONS OF COUPLED HIGGS FIELD EQUATION
TAJIRI, M
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1983, 52 (07) : 2277 - 2280

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