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Approximate Symmetry Reduction for Initial-value Problems of the Extended KdV-Burgers Equations with Perturbation |
| LI Ji-Na1, ZHANG Shun-Li1,2**
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1Center for Nonlinear Studies, Department of Mathematics, Northwest University, Xi'an 710069
2Center of Nonlinear Science, Ningbo University, Ningbo 315211
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| Cite this article: |
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LI Ji-Na, ZHANG Shun-Li 2011 Chin. Phys. Lett. 28 030201 |
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Abstract Approximate generalized conditional symmetry is developed to study the approximate symmetry reduction for initial-value problems of the extended KdV-Burgers equations with perturbation. These equations can be reduced to initial-value problems for some systems of first-order perturbed ordinary differential equations in terms of a new approach. Complete classification theorems are obtained and an example is taken to show the main reduction procedure.
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| Keywords:
02.30.Jr
02.20.Sv
02.30.Ik
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Received: 31 May 2010
Published: 28 February 2011
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[1] Cole J D 1968 Perturbation Methods in Applied Mathematics (Walthma: Blaisdell Publishing Company)
[2] Van Dyke M 1975 Perturbation Methods in Fluid Mechanics (Stanford: CA: Parabolic Press)
[3] Nayfeh A H 2000 Perturbation Methods (New York: John Wiley and Sons)
[4] Olver P J 1993 Applications of Lie Groups to Differential Equations (New York: Springer)
[5] Baikov V A, Gazizov R K and Ibragimov N H 1989 Itogi, Naukii Tekhniki, Seriya Sovremennye probhemy Matematiki, Noveishie Dostizheniya 34 85
[6] Ibragimov N H CRC Handbook of Lie Group Analysis of Differential Equations (Boca Raton, FL: Chemical Rubber Company) vol 3
[7] Baikov V A, Gazizov R K and Ibragimov N H 1988 Math. Sb. 136 435 (Engl. Transl. 1989 Math. USSR Sb. 64 427)
[8] Baikov V A et al 1994 J. Math. Phys. 35 6525
[9] Fushchich W I and Shtelen W M 1999 J. Phys. A: Math. Gen. 22 L887
[10] Mahomed F M and Qu C Z 1999 J. Phys. A: Math. Gen. 33 343
[11] Kara A H et al 2000 J. Phys. A: Math. Gen. 33 6601
[12] Zhang S L and Qu C Z 2006 Chin. Phys. Lett. 23 527
[13] Zhao Y et al 2009 Chin. Phys. Lett. 26 100201
[14] Zhdanov R Z and Andreitsev A Yu 2000 J. Phys. A: Math. Gen. 33 5763
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