一类二阶二次变系数微分算子的不变子空间及其应用  

Invariant Subspaces of a Class of Second-Order Quadratic DiflFerential Operators with Variable Coefficients and Their Applications

作　　者：朱春蓉[1] 吴吟黎 

机构地区：[1]安徽师范大学数学计算机科学学院,芜湖241000

出　　处：《数学学报（中文版）》2016年第5期595-608,共14页Acta Mathematica Sinica：Chinese Series

基　　金：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)

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.In this paper, invariant subspaces of a class of second-order quadratic differ- ential 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.

关 键 词：二阶二次变系数微分算子 不变子空间 精确解 

分 类 号：O175.2[理学—数学]