从无到有II:通过一致关联爆炸的非线性系统
From nothing to something II: nonlinear systems via consistent correlated bang
摘要:
中国古代圣人老子说,一切都来自于\emph{\bf \em "nothing"}。\rm在第一个字母(中国。Phys. Lett. 30(2013)080202),已经通过简单原理(Dao)从“无”获得了无限多个离散可积系统。第二章引入了一个新的概念--相容关联爆炸,得到了一些可积的非线性动力学系统,如连续非线性薛定谔方程(NLS),(势)Korteweg de Vries(KdV)方程,(势)Kadomtsev-Petviashvili(KP)方程和sine-Gordon(sG)方程。这些非线性系统通过适当的“道”、移宇称、电荷共轭、延迟时间反转、移交换、移宇称旋转等方法从无到有。
英文摘要:
Chinese ancient sage Laozi said everything comes from \emph{\bf \em "nothing"}. \rm In the first letter (Chin. Phys. Lett. 30 (2013) 080202), infinitely many discrete integrable systems have been obtained from "nothing" via simple principles (Dao). In this second letter, a new idea, the consistent correlated bang, is introduced to obtain nonlinear dynamic systems including some integrable ones such as the continuous nonlinear Schrödinger equation (NLS), the (potential) Korteweg de Vries (KdV) equation, the (potential) Kadomtsev-Petviashvili (KP) equation and the sine-Gordon (sG) equation. These nonlinear systems are derived from nothing via suitable "Dao", the shifted parity, the charge conjugate, the delayed time reversal, the shifted exchange, the shifted-parity-rotation and so on.
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