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Chin. Phys. B, 2011, Vol. 20(1): 010202    DOI: 10.1088/1674-1056/20/1/010202
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Reductions and conserved quantities for discrete compound KdV–Burgers equations

He Yu-Fang(何玉芳), Liu Yong-Song(刘咏松), and Fu Jing-Li(傅景礼)
Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
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

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