具有微分覆盖的偏微分方程的非局部守恒律
可精确求解与可积系统
2020-09-22 v1
摘要
L. Bianchi 在其 1892 年的论文 [L. Bianchi, Sulla trasformazione di Bäcklund per le superfici pseudosferiche, Rend. Mat. Acc. Lincei, s. 5, v. 1 (1892) 2, 3--12] 中除其他外注意到，描述 sine-Gordon 方程 Bäcklund 变换的公式经过相当简单的变换后，会得到现代语言所称的非局部守恒律。利用微分覆盖的技术 [I.S. Krasil'shchik, A.M. Vinogradov, Nonlocal trends in the geometry of differential equations: symmetries, conservation laws, and Bäcklund transformations, Acta Appl. Math. v. 15 (1989) 1-2, 161--209]，我们表明这一观察具有相当普遍的性质。我们描述了构造此类守恒律的步骤，并给出若干说明性例子。
引用
@article{arxiv.2009.09489,
title = {Nonlocal conservation laws of PDEs possessing differential coverings},
author = {I. Krasil'shchik},
journal= {arXiv preprint arXiv:2009.09489},
year = {2020}
}