Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

doi:10.1088/1674-1056/23/11/110202

›› 2014, Vol. 23 ›› Issue (11): 110202-110202.doi: 10.1088/1674-1056/23/11/110202

Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

屈改珠^{a b}, 张顺利^a, 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

收稿日期:2013-12-26 修回日期:2014-05-14 出版日期:2014-11-15 发布日期:2014-11-15
基金资助:
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).

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

Received:2013-12-26 Revised:2014-05-14 Online:2014-11-15 Published:2014-11-15
Contact: Zhang Shun-Li E-mail:zhangshunli@nwu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: nonlinear evolution equation, quadratic operator, invariant subspace method, blow-up solution

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.

Key words: nonlinear evolution equation, quadratic operator, invariant subspace method, blow-up solution

中图分类号: (Partial differential equations)

02.30.Jr

02.20.Sv (Lie algebras of Lie groups) 02.30.Tb (Operator theory)

屈改珠, 张顺利, 李尧龙. Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension[J]. , 2014, 23(11): 110202-110202.

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[J]. Chin. Phys. B, 2014, 23(11): 110202-110202.

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Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

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