论文标题
汉密尔顿非线性偏微分方程的吸引子
Attractors of Hamiltonian nonlinear partial differential equations
论文作者
论文摘要
我们调查了自1990年出现以来非线性哈密顿局部偏微分方程的吸引子理论。这些是全球吸引对固定状态，孤子和固定轨道的吸引力，对孤子的绝热动态及其渐近稳定性。还给出了数值模拟的结果。基于这些结果，我们提出了一个关于$ g $ invariant非线性汉密尔顿局部微分方程的吸引子的新的一般假设。获得的结果表明，基本量子现象的新型动力学解释：Bohr在量子固定状态，波颗粒二元性和概率解释之间的过渡。
We survey the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. These are results on global attraction to stationary states, to solitons and to stationary orbits, on adiabatic effective dynamics of solitons and their asymptotic stability. Results of numerical simulations are also given. Based on these results, we propose a new general hypothesis on attractors of $G$-invariant nonlinear Hamiltonian partial differential equations. The obtained results suggest a novel dynamical interpretation of basic quantum phenomena: Bohr's transitions between quantum stationary states, wave-particle duality, and probabilistic interpretation.
