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Chin. Phys. B, 2014, Vol. 23(11): 110202    DOI: 10.1088/1674-1056/23/11/110202
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Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

Qu Gai-Zhu (屈改珠)a b, Zhang Shun-Li (张顺利)a, Li Yao-Long (李尧龙)b
a Center for Nonlinear Studies, Department of Mathematics, Northwest University, Xi'an 710069, China;
b School of Mathematics and Information Science, Weinan Normal University, Weinan 714000, China
Abstract  In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.
Keywords:  nonlinear evolution equation      quadratic operator      invariant subspace method      blow-up solution  
Received:  26 December 2013      Revised:  14 May 2014      Accepted manuscript online: 
PACS:  02.30.Jr (Partial differential equations)  
  02.20.Sv (Lie algebras of Lie groups)  
  02.30.Tb (Operator theory)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11371293), the Civil Military Integration Research Foundation of Shaanxi Province, China (Grant No. 13JMR13), the Natural Science Foundation of Shaanxi Province, China (Grant No. 14JK1246), the Mathematical Discipline Foundation of Shaanxi Province, China (Grant No. 14SXZD015), and the Basic Research Project Foundation of Weinan City, China (Grant No. 2013JCYJ-4).
Corresponding Authors:  Zhang Shun-Li     E-mail:  zhangshunli@nwu.edu.cn

Cite this article: 

Qu Gai-Zhu (屈改珠), Zhang Shun-Li (张顺利), Li Yao-Long (李尧龙) Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension 2014 Chin. Phys. B 23 110202

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