Lie symmetries and exact solutions for a short-wave model

doi:10.1088/1674-1056/22/4/040510

中国物理B ›› 2013, Vol. 22 ›› Issue (4): 40510-040510.doi: 10.1088/1674-1056/22/4/040510

Lie symmetries and exact solutions for a short-wave model

陈爱永^a, 章丽娜^b, 温双全^a

a School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China;
b School of Science, Huzhou University, Huzhou 313000, China

收稿日期:2012-09-18 修回日期:2012-11-28 出版日期:2013-03-01 发布日期:2013-03-01
基金资助:
Project supported by the Foundation of Guangxi Key Laboratory of Trusted Software, Guangxi Natural Science Foundation (Grant No. 2011GXNSFA018134) and the National Natural Science Foundation of China (Grant Nos. 11161013 and 61004101).

Lie symmetries and exact solutions for a short-wave model

Chen Ai-Yong (陈爱永)^a, Zhang Li-Na (章丽娜)^b, Wen Shuang-Quan (温双全)^a

a School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China;
b School of Science, Huzhou University, Huzhou 313000, China

Received:2012-09-18 Revised:2012-11-28 Online:2013-03-01 Published:2013-03-01
Contact: Zhang Li-Na E-mail:zsdzln@126.com
Supported by:
Project supported by the Foundation of Guangxi Key Laboratory of Trusted Software, Guangxi Natural Science Foundation (Grant No. 2011GXNSFA018134) and the National Natural Science Foundation of China (Grant Nos. 11161013 and 61004101).

摘要/Abstract

摘要： In this paper, the Lie symmetry analysis and the generalized symmetry method are performed for a short wave model. The symmetries for this equation are given. The phase portraits of the traveling wave systems are analyzed by using the bifurcation theory of dynamical systems. The exact parametric representations of four types of traveling wave solutions are obtained.

关键词: Lie symmetry, short wave model, bifurcation method, loop solution

Abstract: In this paper, the Lie symmetry analysis and the generalized symmetry method are performed for a short-wave model. The symmetries for this equation are given. The phase portraits of the traveling wave systems are analyzed by using the bifurcation theory of dynamical systems. The exact parametric representations of four types of traveling wave solutions are obtained.

Key words: Lie symmetry, short-wave model, bifurcation method, loop solution

中图分类号: (Solitons)

05.45.Yv

02.30.Jr (Partial differential equations) 02.70.-c (Computational techniques; simulations)

陈爱永, 章丽娜, 温双全. Lie symmetries and exact solutions for a short-wave model[J]. 中国物理B, 2013, 22(4): 40510-040510.

Chen Ai-Yong (陈爱永), Zhang Li-Na (章丽娜), Wen Shuang-Quan (温双全). Lie symmetries and exact solutions for a short-wave model[J]. Chin. Phys. B, 2013, 22(4): 40510-040510.

参考文献 28

[1]	Schäfer T and Wayne C 2004 Physica D 19 690
[2]	Matsuno Y 2006 Phys. Lett. A 359 451
[3]	Liu Y 2010 Chin. Phys. Lett. 27 090201
[4]	Huang L 2006 Chin. Phys. Lett. 23 4
[5]	Zhang J F and Yang Q 2005 Chin. Phys. Lett. 22 1855
[6]	Liu C S 2004 Chin. Phys. Lett. 21 2369
[7]	Ying J P and Lou S Y 2003 Chin. Phys. Lett. 20 1448
[8]	Biswas A, Yildirim A, Hayat T, Aldossary O and Sassaman R 2012 Proceedings of the Romanian Academy, Series A 13 32
[9]	Johnpillai A, Yildirim A and Biswas A 2012 Rom. J. Phys. 57 545
[10]	Triki H, Yildirim A, Hayat T, Aldossary O and Biswas A 2012 Rom. J. Phys. 57 1029
[11]	Lou S Y, Tang X Y and Chen C L 2002 Chin. Phys. Lett. 19 769
[12]	Ma Y L, Xu M P and Li B Q 2010 Acta Phys. Sin. 59 1409 (in Chinese)
[13]	Triki H, Yildirim A, Hayat T, Aldossary O and Biswas A 2012 Rom. Rep. Phys. 64 672
[14]	Biswas A, Khan K, Rahaman A, Yildirim A, Hayat T and Aldossary O 2012 J. Optoelectron. Adv. Mater. 14 571
[15]	Zhang J F and Wu F M 1999 Chin. Phys. 8 326
[16]	Lou S Y 1997 Chin. Phys. 6 561
[17]	Olver P 1993 Applications of Lie Groups to Differential Equations, in Grauate Texts in Mathematics, Vol. 107 (New York: Springer)
[18]	Bluman G and Kumei S 1989 Symmetries and Differential Equations (Berlin: Springer-Verlag)
[19]	Lou S Y 1994 J. Math. Phys. 35 2390
[20]	Liu H Z and Li J B 2009 Nonlinear Anal. 71 2126
[21]	Qu C Z 2007 J. Phys. A: Math. Theor. 40 1757
[22]	Kang J and Qu C Z 2002 J. Math. Phys. 53 023509
[23]	Li J B and Dai H H 2007 On the Study of Singular Nonlinear Traveling Wave Equations: Dynamical System Approach (Beijing: Science Press)
[24]	Li J B and Zhang Y 2009 Nonlinear Anal.: Real World Appl. 10 2502
[25]	Feng D H and Li J B 2007 Phys. Lett. A 369 255
[26]	Zhang L N and Li J B 2011 Phys. Lett. A 375 2965
[27]	Bruzón M, Gandarias M, González G and Hansen R 2012 Appl. Math. Comput. 218 10094
[28]	Chen A Y and Li J B 2010 J. Math. Anal. Appl. 369 758

Lie symmetries and exact solutions for a short-wave model

Lie symmetries and exact solutions for a short-wave model

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 28

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Hengchun Hu(胡恒春) and Yaqi Li(李雅琦). Lie symmetry analysis and invariant solutions for the (3+1)-dimensional Virasoro integrable model[J]. 中国物理B, 2023, 32(4): 40503-040503.
[2]	孙毅, 陈本永, 傅景礼. Lie symmetry theorem of fractional nonholonomic systems[J]. , 2014, 23(11): 110201-110201.
[3]	王肖肖, 韩月林, 张美玲, 贾利群. Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints[J]. 中国物理B, 2013, 22(2): 20201-020201.
[4]	方建会,张斌,张伟伟,徐瑞莉. Mei conserved quantity directly induced by Lie symmetry in a nonconservative Hamilton system[J]. 中国物理B, 2012, 21(5): 50202-050202.
[5]	施沈阳, 傅景礼. Lie symmetry and Mei conservation law of continuum system[J]. 中国物理B, 2011, 20(2): 21101-021101.
[6]	张美玲, 孙现亭, 王肖肖, 解银丽, 贾利群. Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion[J]. 中国物理B, 2011, 20(11): 110202-110202.
[7]	解银丽, 贾利群, 罗绍凯. Special Lie symmetry and Hojman conserved quantity of Appell equations in a dynamical system of relative motion[J]. 中国物理B, 2011, 20(1): 10203-010203.
[8]	方建会. A new type of conserved quantity of Lie symmetry for the Lagrange system[J]. 中国物理B, 2010, 19(4): 40301-040301.
[9]	赵丽, 傅景礼, 陈本永. Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration[J]. 中国物理B, 2010, 19(1): 10301-010301.
[10]	吕洪升, 张宏彬, 顾书龙. Hojman's theorem of the third-order ordinary differential equation[J]. 中国物理B, 2009, 18(8): 3135-3138.
[11]	丁宁, 方建会, 陈相霞. Perturbation to Lie symmetry and another type of Hojman adiabatic invariants for Birkhoffian systems[J]. 中国物理B, 2008, 17(6): 1967-1971.
[12]	施沈阳, 黄晓虹. Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates[J]. 中国物理B, 2008, 17(5): 1554-1559.
[13]	施沈阳, 傅景礼, 黄晓虹, 陈立群, 张晓波. The Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass[J]. 中国物理B, 2008, 17(3): 754-758.
[14]	施沈阳, 傅景礼, 陈立群. The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems[J]. 中国物理B, 2008, 17(2): 385-389.
[15]	蔺鹏, 方建会, 庞婷. Lie symmetry and Hojman conserved quantity of Nambu system[J]. 中国物理B, 2008, 17(12): 4361-4364.