Approximate Symmetry Reduction for Initial-value Problems of the Extended KdV-Burgers Equations with Perturbation
LI Ji-Na1, ZHANG Shun-Li1,2**
1Center for Nonlinear Studies, Department of Mathematics, Northwest University, Xi'an 710069 2Center of Nonlinear Science, Ningbo University, Ningbo 315211
Approximate Symmetry Reduction for Initial-value Problems of the Extended KdV-Burgers Equations with Perturbation
LI Ji-Na1, ZHANG Shun-Li1,2**
1Center for Nonlinear Studies, Department of Mathematics, Northwest University, Xi'an 710069 2Center of Nonlinear Science, Ningbo University, Ningbo 315211
摘要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.
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.
LI Ji-Na;ZHANG Shun-Li;**
. Approximate Symmetry Reduction for Initial-value Problems of the Extended KdV-Burgers Equations with Perturbation[J]. 中国物理快报, 2011, 28(3): 30201-030201.
LI Ji-Na, ZHANG Shun-Li, **
. Approximate Symmetry Reduction for Initial-value Problems of the Extended KdV-Burgers Equations with Perturbation. Chin. Phys. Lett., 2011, 28(3): 30201-030201.
[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