Chin. Phys. Lett.  2011, Vol. 28 Issue (3): 030201    DOI: 10.1088/0256-307X/28/3/030201
GENERAL |
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
Cite this article:   
LI Ji-Na, ZHANG Shun-Li 2011 Chin. Phys. Lett. 28 030201
Download: PDF(430KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
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.
Keywords: 02.30.Jr      02.20.Sv      02.30.Ik     
Received: 31 May 2010      Published: 28 February 2011
PACS:  02.30.Jr (Partial differential equations)  
  02.20.Sv (Lie algebras of Lie groups)  
  02.30.Ik (Integrable systems)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/28/3/030201       OR      https://cpl.iphy.ac.cn/Y2011/V28/I3/030201
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
LI Ji-Na
ZHANG Shun-Li
[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
Related articles from Frontiers Journals
[1] E. M. E. Zayed, S. A. Hoda Ibrahim. Exact Solutions of Nonlinear Evolution Equations in Mathematical Physics Using the Modified Simple Equation Method[J]. Chin. Phys. Lett., 2012, 29(6): 030201
[2] WU Yong-Qi. Exact Solutions to a Toda-Like Lattice Equation in 2+1 Dimensions[J]. Chin. Phys. Lett., 2012, 29(6): 030201
[3] CUI Kai. New Wronskian Form of the N-Soliton Solution to a (2+1)-Dimensional Breaking Soliton Equation[J]. Chin. Phys. Lett., 2012, 29(6): 030201
[4] CAO Ce-Wen**,ZHANG Guang-Yao. Lax Pairs for Discrete Integrable Equations via Darboux Transformations[J]. Chin. Phys. Lett., 2012, 29(5): 030201
[5] DAI Zheng-De**, WU Feng-Xia, LIU Jun and MU Gui. New Mechanical Feature of Two-Solitary Wave to the KdV Equation[J]. Chin. Phys. Lett., 2012, 29(4): 030201
[6] Mohammad Najafi**,Maliheh Najafi,M. T. Darvishi. New Exact Solutions to the (2+1)-Dimensional Ablowitz–Kaup–Newell–Segur Equation: Modification of the Extended Homoclinic Test Approach[J]. Chin. Phys. Lett., 2012, 29(4): 030201
[7] HUANG Chao-Guang,**,TIAN Yu,WU Xiao-Ning,XU Zhan,ZHOU Bin. New Geometry with All Killing Vectors Spanning the Poincaré Algebra[J]. Chin. Phys. Lett., 2012, 29(4): 030201
[8] S. Karimi Vanani, F. Soleymani. Application of the Homotopy Perturbation Method to the Burgers Equation with Delay[J]. Chin. Phys. Lett., 2012, 29(3): 030201
[9] WANG Jun-Min. Periodic Wave Solutions to a (3+1)-Dimensional Soliton Equation[J]. Chin. Phys. Lett., 2012, 29(2): 030201
[10] ZHENG Shi-Wang, WANG Jian-Bo, CHEN Xiang-Wei, XIE Jia-Fang. Mei Symmetry and New Conserved Quantities of Tzénoff Equations for the Variable Mass Higher-Order Nonholonomic System[J]. Chin. Phys. Lett., 2012, 29(2): 030201
[11] Hermann T. Tchokouansi, Victor K. Kuetche, Abbagari Souleymanou, Thomas B. Bouetou, Timoleon C. Kofane. Generating a New Higher-Dimensional Ultra-Short Pulse System: Lie-Algebra Valued Connection and Hidden Structural Symmetries[J]. Chin. Phys. Lett., 2012, 29(2): 030201
[12] LIU Ping**, FU Pei-Kai. Note on the Lax Pair of a Coupled Hybrid System[J]. Chin. Phys. Lett., 2012, 29(1): 030201
[13] LOU Yan, ZHU Jun-Yi** . Coupled Nonlinear Schrödinger Equations and the Miura Transformation[J]. Chin. Phys. Lett., 2011, 28(9): 030201
[14] WANG Jun-Min**, YANG Xiao . Theta-function Solutions to the (2+1)-Dimensional Breaking Soliton Equation[J]. Chin. Phys. Lett., 2011, 28(9): 030201
[15] A H Bokhari, F D Zaman, K Fakhar, *, A H Kara . A Note on the Invariance Properties and Conservation Laws of the Kadomstev–Petviashvili Equation with Power Law Nonlinearity[J]. Chin. Phys. Lett., 2011, 28(9): 030201
Viewed
Full text


Abstract