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一类非线性波动方程的势对称分类

特木尔朝鲁(1), 张智勇(2)   

  1. (1)上海海事大学数学系, 上海 200135; (2)中国科学院研究生院数学科学学院, 北京 100049.
  • 收稿日期:2006-12-06 修回日期:2007-12-17 出版日期:2009-03-25 发布日期:2009-03-25

特木尔朝鲁;张智勇. 一类非线性波动方程的势对称分类[J]. 系统科学与数学, 2009, 29(3): 389-411.

Temuerchaolu;ZHANG Zhiyong. Potential Symmetry Classification for a Class of Nonlinear Wave Equations[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(3): 389-411.

Potential Symmetry Classification for a Class of Nonlinear Wave Equations

Temuerchaolu(1), ZHANG Zhiyong(2)   

  1. (1)College of Mathematics, Shanghai Marinetime University, Shanghai 200135; (2)School of Mathematical Science, Graduate University of Chinese Academy of Science, Beijing 100049.
  • Received:2006-12-06 Revised:2007-12-17 Online:2009-03-25 Published:2009-03-25
先给出了含有一个任意函数的线性波动方程的古典和势对称的完全分类.然后,在此基础上给出了含有两个任意函数的一类非线性波动方程的两种情形势对称分类,得到了该方程的新势对称.在处理对称群分类问题的难点-求解确定方程组时我们提出了微分形式吴方法算法,克服了以往难于处理的困难.在整个计算过程中反复使用了吴方法,吴方法起到了关键的作用.
In this paper, a complete classical and potential symmetry classification is obtained for a linear wave equation containing an arbitrary function. Then based on the results, two kinds of potential symmetry classifications, through two equivalent equations, are determined for a scalar nonlinear wave equation with two arbitrary functions. As a result, new potential symmetries of this equation are given. The most difficult problem existing in current calculations for symmetry group classifications, i.e., solving over-determined determining equations, is overcomed by using differential form Wu's method algorithm. The method is used repeatly in whole huge calculations and plays key rule.

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[1] 陈金梅, 王祥. 一类非线性波动方程弱解的存在唯一性[J]. 系统科学与数学, 2011, 31(8): 985-991.
[2] 张智勇;雍雪林;陈玉福. 一类组合方程的势对称分类[J]. 系统科学与数学, 2008, 28(8): 905-914.
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