李氏减阶算法对 ODE 的自然扩展

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-12 DOI:arxiv-2407.09063

George W. Bluman, Rafael de la Rosa

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引用次数: 0

摘要

在本文中，我们进一步探讨了基于对称性的偏微分方程求非局部相关系统的方法。特别是，我们通过从不同的角度观察李氏常微分方程的降阶算法，证明基于对称性的偏微分方程方法是该算法的自然扩展。许多例子展示了可能出现的各种情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The natural extension to PDEs of Lie's reduction of order algorithm for ODEs

In this paper, we further consider the symmetry-based method for seeking nonlocally related systems for partial differential equations. In particular, we show that the symmetry-based method for partial differential equations is the natural extension of Lie's reduction of order algorithm for ordinary differential equations by looking at this algorithm from a different point of view. Many examples exhibit various situations that can arise.

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arXiv - MATH - Classical Analysis and ODEs

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