微分方程对称的符号计算实用指南
Practical Guide to the Symbolic Computation of Symmetries of Differential Equations
摘要：
对称性在寻找非线性微分方程的解析解中起着至关重要的作用。对称性是微分方程的解到解的映射，并且已经被广泛研究了一个多世纪。我们提出了一种计算方法来寻找对称性和计算机代数程序来计算通常非常大的系统，确定偏微分方程。我们还提供了计算机代数算法，至少可以自动解决大多数这些方程，并在简单的情况下提供一个完整的解决方案。这些算法是在maxima/wxmaxima中编程的，可以免费获得。
英文摘要：
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a century. We present a computational approach to finding symmetries and computer algebra programs to compute the usually very large system of determining partial differential equations. We also provide computer algebra algorithm that at least automatically solves most of these equations and in simple cases provides a complete solution. The algorithms are programmed in maxima/wxmaxima that is freely available.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
