Lou S Y, Huang Fei
Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China.
Ningbo Collabrative Innovation Center of Nonlinear Harzard System of Ocean and Atmosphere and Faculty of Science, Ningbo University, Ningbo, 315211, China.
Sci Rep. 2017 Apr 13;7(1):869. doi: 10.1038/s41598-017-00844-y.
In natural and social science, many events happened at different space-times may be closely correlated. Two events, A (Alice) and B (Bob) are defined correlated if one event is determined by another, say, [Formula: see text] for suitable [Formula: see text] operators. Taking KdV and coupled KdV systems as examples, we can find some types of models (AB-KdV systems) to exhibit the existence on the correlated solutions linked with two events. The idea of this report is valid not only for physical problems related to KdV systems but also for problems described by arbitrary continuous or discrete models. The parity and time reversal symmetries are extended to shifted parity and delayed time reversal. The new symmetries are found to be useful not only to establish AB-systems but also to find group invariant solutions of numerous AB-systems. A new elegant form of the N-soliton solutions of the KdV equation and then the AB-KdV systems is obtained. A concrete AB-KdV system derived from the nonlinear inviscid dissipative and barotropic vorticity equation in a β-plane channel is applied to the two correlated monople blocking events which is responsible for the snow disaster in the winter of 2007/2008 happened in Southern China.
在自然科学和社会科学中，许多发生在不同时空的事件可能紧密相关。如果一个事件由另一个事件决定，比如说，对于合适的[公式：见原文]算子，有[公式：见原文]，那么两个事件A（爱丽丝）和B（鲍勃）就被定义为相关的。以KdV和耦合KdV系统为例，我们可以找到一些类型的模型（AB - KdV系统）来展示与两个事件相关的相关解的存在性。本报告的想法不仅对与KdV系统相关的物理问题有效，而且对由任意连续或离散模型描述的问题也有效。宇称和时间反演对称性被扩展到移位宇称和延迟时间反演。发现新的对称性不仅有助于建立AB系统，而且有助于找到众多AB系统的群不变解。得到了KdV方程以及AB - KdV系统的N孤子解的一种新的优美形式。一个由β平面通道中的非线性无粘耗散和正压涡度方程导出的具体AB - KdV系统被应用于两个相关的单极阻塞事件，这两个事件导致了2007/2008年冬季发生在中国南方的雪灾。
