| 一类二阶二次变系数微分算子的不变子空间及其应用 |
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| 引用本文： | 朱春蓉,吴吟黎. 一类二阶二次变系数微分算子的不变子空间及其应用[J]. 数学学报, 2016, 59(5): 595-608 |
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| 作者姓名： | 朱春蓉 吴吟黎 |
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| 作者单位： | 安徽师范大学数学计算机科学学院 芜湖 241000 |
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| 基金项目： | 国家自然科学基金资助项目（11301007）；安徽省自然科学基金资助项目（1408085QA05） |
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| 摘 要： | 研究了一类二阶二次变系数微分算子的不变子空间,讨论了这类微分算子不变子空间的应用,并给出了具体应用的一些例子.在这些例子中,构造了大量变系数非线性演化方程的精确解.
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| 关 键 词： | 二阶二次变系数微分算子 不变子空间 精确解 |
Invariant Subspaces of a Class of Second-Order Quadratic Differential Operators with Variable Coefficients and Their Applications |
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| Chun Rong,ZHU Yin Li WU. Invariant Subspaces of a Class of Second-Order Quadratic Differential Operators with Variable Coefficients and Their Applications[J]. Acta Mathematica Sinica, 2016, 59(5): 595-608 |
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| Authors: | Chun Rong ZHU Yin Li WU |
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| Affiliation: | College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, P. R. China |
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| Abstract: | In this paper, invariant subspaces of a class of second-order quadratic differential operators with variable coefficients are described. Applications of these invariant subspaces are discussed. Some examples are presented to illustrate their applications. In these examples, exact solutions of many nonlinear evolution equations with variable coefficients are constructed. |
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| Keywords: | second-order quadratic differential operators with variable coefficients invariant subspaces exact solutions |
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