论文标题
正弦戈登在虫洞上
Sine-Gordon on a wormhole
论文作者
论文摘要
为了理解孤子分辨率的猜想，我们考虑了球形对称的虫洞空间上的正弦 - 戈登方程。我们表明，在每个拓扑领域（由积极的整数$ n $索引）中存在一个独特的线性稳定孤子，我们称之为$ n $ -kink。我们提供的数值证据表明，$ n $ kink是任何流畅，有限的能源解决方案$ n $的全球吸引子。当蠕虫喉咙$ a $的半径足够大时，与$ n $ kink的收敛被证明是由内部模式支配的，由于能量将能量引起的辐射传递引起，这些模式缓慢衰减。我们使用柔软的非线性扰动理论计算了$ 1 kink的这种放松过程的确切渐近过程。
In an attempt to understand the soliton resolution conjecture, we consider the Sine-Gordon equation on a spherically symmetric wormhole spacetime. We show that within each topological sector (indexed by a positive integer degree $n$) there exists a unique linearly stable soliton, which we call the $n$-kink. We give numerical evidence that the $n$-kink is a global attractor in the evolution of any smooth, finite energy solutions of degree $n$. When the radius of the wormhole throat $a$ is large enough, the convergence to the $n$-kink is shown to be governed by internal modes that slowly decay due to the resonant transfer of energy to radiation. We compute the exact asymptotics of this relaxation process for the $1$-kink using the Soffer-Weinstein weakly nonlinear perturbation theory.
