Approximate Symmetry Reduction and Infinite Series Solutions to the Nonlinear Wave Equation with Damping

doi:10.1088/0256-307X/26/10/100201

Chin. Phys. Lett.

2009, Vol. 26

Issue (10): 100201 DOI: 10.1088/0256-307X/26/10/100201

GENERAL

Approximate Symmetry Reduction and Infinite Series Solutions to the Nonlinear Wave Equation with Damping

ZHAO Yuan¹, ZHANG Shun-Li^1,3, LOU Sen-Yue^2,3

¹Center for Nonlinear Studies, Department of Mathematics, Northwest University, Xi'an 710069²Department of Physics, Shanghai Jiao Tong University, Shanghai 200240³Department of Physics, Ningbo University, Ningbo 315211

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ZHAO Yuan, ZHANG Shun-Li, LOU Sen-Yue 2009 Chin. Phys. Lett. 26 100201

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Abstract The approximate symmetry perturbation method is applied to the nonlinear damped wave equation. The approximate symmetry reduction equations of different orders are derived and the corresponding series reduction solutions are obtained.

Keywords: 02.30.Jr

Received: 02 June 2009 Published: 27 September 2009

PACS:

02.30.Jr

(Partial differential equations)

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https://cpl.iphy.ac.cn/10.1088/0256-307X/26/10/100201 OR https://cpl.iphy.ac.cn/Y2009/V26/I10/100201

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[1] Cole J D 1968 Perturbation Methods in AppliedMathematics (Walthma: Blaisdell Publishing Company)
[2] Van Dyke M 1975 Perturbation Methods in FluidMechanics (Stanford: CA: Parabolic Press)
[3] Nayfeh A H 2000 Perturbation Methods (New York:John Wiley and Sons)
[4] Baikov V A, Gazizov R K and Ibragimov N H 1988 Mat.Sb. 136 435
[5] Fushchich W I and Shtelen W M 1989 J. Phys. A: Math.Gen. 22 L887
[6] Pakdemirli M, Yurusoy M and Dolapci I T 2004 ActaAppl. Math. 80 243
[7] Wiltshire R 2006 J. Comput. Appl. Math. 197287
[8] Clarkson P A and Kruskal M D 1989 J. Math. Phys. 30 2201
[9] Lou S Y 1990 Phys. Lett. A 151 133
[10] Olver P J 1993 Applications of Lie Groups to Differential Equations (New York: Springer) Bluman G W and Kumei S 1989 Symmetries and DifferentialEquations (New York: Springer) Ibragimov Kh N 1985 Transformation Groups Applied toMathematical Physics (Dordrecht: Reidel)
[11] Jiao X Y, Yao R X and Lou S Y 2008 J. Math. Phys. 49 093505
[12] Jiao X Y, Yao R X, Zhang S L and Lou S Y 2008 arXiv:0801.0856v2
[nlin.SI]
[13] Jia M, Wang J Y and Lou S Y 2009 Chin. Phys. Lett. 26 020201
[14] Jiao X Y, Yao R X and Lou S Y 2009 Chin. Phys.Lett. 26 040202
[15] Ahmad F, Kara A H, Bokhari A H and Zaman F D 2008 Appl. Math. Comput. 206 16

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