接触细菌和偏微分方程

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-04-02 DOI:arxiv-2404.01955

O. V. Kaptsov

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引用次数: 0

摘要

文章介绍了将某些偏微分方程的解转化为其他方程的解的接触萌芽。文章定义了微分方程的参数对称性，概括了点对称性和接触对称性。新的变换和对称性可能取决于任意但有限阶的导数。以静态薛定谔方程、声学方程和气体动力学方程为例进行了讨论。

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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Contact germs and partial differential equations

The article introduces contact germs that transform solutions of some partial differential equations into solutions of other equations. Parametric symmetries of differential equations generalizing point and contact symmetries are defined. New transformations and symmetries may depend on derivatives of arbitrary but finite order. The stationary Schr\"odinger equations, acoustics and gas dynamics equations are considered as examples.

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arXiv - PHYS - Exactly Solvable and Integrable Systems

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