Reductions and conserved quantities for discrete compound KdV–Burgers equations

doi:10.1088/1674-1056/20/1/010202

Abstract We present two methods to reduce the discrete compound KdV–Burgers equation, which are reductions of the independent and dependent variables: the translational invariant method has been applied in order to reduce the independent variables; and a discrete spectral matrix has been introduced to reduce the number of dependent variables. Based on the invariance of a discrete compound KdV–Burgers equation under infinitesimal transformation with respect to its dependent and independent variables, we present the determining equations of transformation Lie groups for the KdV–Burgers equation and use the characteristic equations to obtain new forms of invariants.

Keywords: discrete compound KdV–Burgers equation symmetry reduction invariant

Received: 08 March 2010
Revised: 25 September 2010
Accepted manuscript online:

PACS:	02.20.-a	(Group theory)
	02.30.Ks	(Delay and functional equations)
	04.50.+h

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 10672143).

Cite this article:

He Yu-Fang(何玉芳), Liu Yong-Song(刘咏松), and Fu Jing-Li(傅景礼) Reductions and conserved quantities for discrete compound KdV–Burgers equations 2011 Chin. Phys. B 20 010202

[1]	Olver P 1993 Applications of Lie Groups to Differential Equations (New York: Springer)
[2]	Bluman G W and Kumei S 1989 Symmetries of Differential Equations (Berlin: Springer)
[3]	Hydon P 1999 Symmetry Methods for Ordinary Differential Equations (Cambridge: Cambridge University Press)
[4]	Mei F X 1999 Applications of Lie Group and Lie Algebra to Constraint Mechanical Systems (Beijing: Science Press)
[5]	Ovisiannikov L V 1982 Group Analysis of Difference Equations (New York: Academic)
[6]	Hern'andez Heredero R, Levi D and Winternitz P 1999 J. Phys. A: Math. Gen. 32 2685
[7]	Rodr'higuez M A and Winternitz P 2004 J. Phys. A: Math. Gen. 37 6129
[8]	Dorodnitsyn V, Kozlov R and Winternitz P 2004 J. Math. Phys. 45 336
[9]	Nucci M.C, Leach P G L and Andriopoulos K 2006 J. Math. Anal. Appl. 319 357
[10]	Boutros Y Z, Abd-el-Malek M B, Badran N A and Hassan H S 2007 Appl. Math. Mode. 31 1092
[11]	Hernandez Heredero R, Levi D, Petrera M and Scimiterna C 2007 J. Phys. A: Math. Theor. 40 831
[12]	Pakdemirli M, Dolapcchi I T and Yhilba B S 2007 Int. J. Thermal Sciences 46 908
[13]	Mei F X 2001 Chin. Phys. 10 177
[14]	Maeda S 1980 Math. Jpn. 25 405
[15]	Fu J L, Dai G D, Jimenez S and Tang Y F 2007 Chin. Phys. 16 570
[16]	Dorodnitsyn V A 2001 Appl. Numer. Math. 39 307
[17]	Johnson R S 1970 J. Fluid Mech. 42 49
[18]	Canosa J and Gazdag J 1977 J. Comput. Phys. 23 393
[19]	Parkes E J and Duffy B R 1996 Comp. Phys. Commun. 98 288
[20]	Cariello F and Tabor M 1989 Physica D 39 77
[21]	Lu B Q, Xiu B Z, Pang Z L and Jiang X F 1993 Phys. Lett. A 175 113
[22]	Liu C, Mei F X and Guo Y X 2009 Chin. Phys. B 18 395
[23]	Chen Y D, Li L, Zhang Y and Hu J M 2009 Chin. Phys. B 18 1373
[24]	Shang M and Mei F X 2009 Chin. Phys. B 18 3155
[25]	Fu J L, Chen B Y and Xie F P 2008 Chin. Phys. B 17 4354
[26]	Zhang H B, Chen L Q and Liu R W 2005 Chin. Phys. 14 238
[27]	Chen X W, Liu C M and Liu Y M 2006 Chin. Phys. 15 470
[28]	Lou Z M 2006 Chin. Phys. 15 891
[29]	Fang J H, Liao Y P, Ding N and Wang P 2006 Chin. Phys. 15 2792
[30]	Guo Y X, Jing L Y and Yu Y 2001 Chin. Phys. 10 181
[31]	Zhang Y, Shang M and Mei F X 2000 Chin. Phys. 9 401
[32]	Zhang H B, Chen L Q and Liu R W 2005 Chin. Phys. 14 888
[33]	Zhang H B, Chen L Q and Liu R W 2005 Chin. Phys. 15 249
[34]	Zhang M J, Fang J H, Zhang X N and Lu K 2008 Chin. Phys. B 17 1957
[35]	Bluman G W and Kumei S 1991 Symmetries and Differential Equations (Beijing: World Publishing Corporation) p80
[36]	Xia L L, Cai J L and Li Y C 2009 Chin. Phys. B 18 3158
[37]	Li R J, Qiao Y F and Zhao S H 2006 Acta Phys. Sin. 55 5598 (in Chinese) endfootnotesize

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Reductions and conserved quantities for discrete compound KdV–Burgers equations

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