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

作　　者：屈改珠 张顺利 李尧龙 

机构地区：[1]Center for Nonlinear Studies Department of Mathematics Northwest University [2]School of Mathematics and Information Science Weinan Normal University

出　　处：《Chinese Physics B》2014年第11期118-124,共7页中国物理B（英文版）

基　　金：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);the Basic Research Project Foundation of Weinan City,China(Grant No.2013JCYJ-4)

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.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 

分 类 号：O175[理学—数学] O177.1[理学—基础数学]