GROUP-INVARIANT SOLUTIONS OF DIFFERENTIAL-EQUATIONS

被引：199

作者：

OLVER, PJ ^{[1
]}

ROSENAU, P ^{[1
]}

机构：

[1] TECHNION ISRAEL INST TECHNOL,DEPT MECH ENGN,IL-32000 HAIFA,ISRAEL

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 1987年 / 47卷 / 02期

关键词：

D O I：

10.1137/0147018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the concept of a weak symmetry group of a system of partial differential equations, that generalizes the 'nonclassical' method introduced by G. W. Bluman and J. D. Cole for finding group-invariant solutions to partial differential equations. Given any system of partial differential equations, it is shown how, in principle, to construct group-invariant solutions for any group of transformations by reducing the number of variables in the system. Conversely, every solution of the system can be found using this reduction method with some weak symmetry group.

引用

页码：263 / 278

页数：16

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