论文标题
具有差异覆盖物的PDE的非本地保护法
Nonlocal conservation laws of PDEs possessing differential coverings
论文作者
论文摘要
在他的1892年论文中[L. bianchi，sulla trasformazione dibäcklundper le cartecudosferiche，摘要。垫。 ACC。 Lincei，s。 5，v。1（1892）2，3--12]，L。Bianchi注意到，除其他外，它描述了正弦 - 戈登方程的Bäcklund转换的非常简单的转换，导致了现代语言中所谓的非局限性保护法。使用差分覆盖物的技术[I.S. Krasil'shchik，A.M。 Vinogradov，微分方程几何形状的非本地趋势：对称性，保护定律和Bäcklund变换，Acta Appl。数学。 v。15（1989）1-2，161--209]，我们表明这种观察性质是相当一般的。我们描述了构建此类保护法的程序并提出了许多说明性示例。
In his 1892 paper [L. Bianchi, Sulla trasformazione di Bäcklund per le superfici pseudosferiche, Rend. Mat. Acc. Lincei, s. 5, v. 1 (1892) 2, 3--12], L. Bianchi noticed, among other things, that quite simple transformations of the formulas that describe the Bäcklund transformation of the sine-Gordon equation lead to what is called a nonlocal conservation law in modern language. Using the techniques of differential coverings [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], we show that this observation is of a quite general nature. We describe the procedures to construct such conservation laws and present a number of illustrative examples.
