论文标题
非线性klein-gordon方程的时空通气解决方案
Space-time breather solution for nonlinear Klein-Gordon equations
论文作者
论文摘要
klein-gordon方程描述了亚原子尺度中波/粒子的动力学。对于非线性klein-gordon方程，它们的呼吸溶液通常被称为具有消失空间结合条件的时间周期溶液。呼吸溶液的存在是正弦 - 戈登方程的知名度，而正弦式方程也称为孤子方程。呼吸溶液是某种时间周期性解决方案，不仅在混乱动力学的桥接路径中起着至关重要的作用，而且在相位空间内提供了多维封闭环。在本文中，基于高精度数值方案，研究了具有周期性边界条件的非线性klein-gordon方程的呼气模式的外观。施加了空间周期性边界条件，以使我们范围中的呼吸型解决方案在时间和空间方面是周期性的。总之，提出了时空周期溶液的存在条件，并显示了无限维动力系统内部的紧凑型歧管。 Klein-Gordon方程的时空通气解决方案可能是亚原子非线性动力学的基本构建基础。
Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For nonlinear Klein-Gordon equations, their breather solutions are usually known as time periodic solutions with the vanishing spatial-boundary condition. The existence of breather solution is known for the Sine-Gordon equations, while the Sine-Gordon equations are also known as the soliton equation. The breather solutions is a certain kind of time periodic solutions that are not only play an essential role in the bridging path to the chaotic dynamics, but provide multi-dimensional closed loops inside phase space. In this paper, based on the high-precision numerical scheme, the appearance of breather mode is studied for nonlinear Klein-Gordon equations with periodic boundary condition. The spatial periodic boundary condition is imposed, so that the breathing-type solution in our scope is periodic with respect both to time and space. In conclusion, the existence condition of space-time periodic solution is presented, and the compact manifolds inside the infinite-dimensional dynamical system is shown. The space-time breather solutions of Klein-Gordon equations can be a fundamental building block for the sub-atomic nonlinear dynamics.
