摘要
给出（偏）微分方程（组）（PDEs）对称向量的吴-微分特征列集（消元）算法理论．把古典和非古典PDEs对称问量的计算问题统-在吴-微分特征列理论框架之下处理．给出了产生PDEs对称向量的无穷小方程和验证已知向量为PDES对称向量的机械化原理，理论上彻底克服了传统算法中的缺陷并为计算PDEs对称向量提供了一种新算法．用计算机代数系统mathematica编制了相应的软件包，具体实现了该算法．作为应用给出了Burgers方程的非古典对称向量的完整解答．
In this paper, The Wu-differential characteristic set algorithm for computations symmetries of partial differential equations (PDEs) and the united theoretic framework for determination of classical and non-classical symmetries of PDEs are put forwarded, The algorithm always yield all Determining equatins (D. Es) of symmetry of the considering PDEs and makes the “super large scale” D. Es equivalently reduce to “smaller scale” set of differential equaitons and therefore significantly decrease the computational efforts of solv-ing D. Es. Also a principle of Mechanical symmetry computing and testing of PDEs’ sym-metry is given. As an application of our algorithm, completely nonclassical symmetries of Burgers equation are calculated.
出处
《数学物理学报（A辑）》
CSCD
北大核心
1999年第3期326-332,共7页
Acta Mathematica Scientia
基金
国家自然科学基金!19861003
