论文标题
$bφ^{4} $模型中的扭结散射
Scattering of kinks in the $Bφ^{4}$ model
论文作者
论文摘要
在这项研究中，基于$φ^4 $模型，引入了一种新型号（称为$bφ^4 $模型），其中尺寸大于$ 1 $的田地值的潜在形式乘以正数$ b $。与单个扭结（Antikink）解决方案有关的所有功能都保持不变，并且独立于参数$ b $。但是，当扭结与碰撞中的抗Kink相互作用时，结果将大大取决于参数$ b $。因此，对于扭结 - 安提奇克碰撞，许多功能，例如临界速度，固定初始速度的输出速度，两次弹跳逃生窗口，极端值和分形结构在参数$ b $方面都是详细考虑的。明确证实了参数$ b $在扭结碰撞中几乎孤子行为的出现中的作用。可以看到逃生窗口图中的分形结构，用于制度$ b \ leq 1 $。但是，对于制度$ b> 1 $，随着$ b = 3.3 $，这种行为逐渐变得模糊和混乱。 CASE $ B = 3.3 $再次获得为关键速度曲线的最小值作为$ B $的函数。对于制度$ 3.3 <b \ leq 10 $，混乱的行为逐渐减少。但是，从未观察到分形结构。然而，这表明，尽管逃生窗的模糊和改组，但它们遵循共鸣能量交换理论的规则。
In this study, based on the $φ^4$ model, a new model (called the $Bφ^4$ model) is introduced in which the potential form for the values of the field whose magnitudes are greater than $1$ is multiplied by the positive number $B$. All features related to a single kink (antikink) solution remain unchanged and are independent of parameter $B$. However, when a kink interacts with an antikink in a collision, the results will significantly depend on parameter $B$. Hence, for kink-antikink collisions, many features such as the critical speed, output velocities for a fixed initial speed, two-bounce escape windows, extreme values, and fractal structure in terms of parameter $B$ are considered in detail numerically. The role of parameter $B$ in the emergence of a nearly soliton behavior in kink-antikink collisions at some initial speed intervals is clearly confirmed. The fractal structure in the diagrams of escape windows is seen for the regime $B\leq 1$. However, for the regime $B >1$, this behavior gradually becomes fuzzing and chaotic as it approaches $B = 3.3$. The case $B = 3.3$ is obtained again as the minimum of the critical speed curve as a function of $B$. For the regime $3.3< B \leq 10$, the chaotic behavior gradually decreases. However, a fractal structure is never observed. Nevertheless, it is shown that despite the fuzzing and shuffling of the escape windows, they follow the rules of the resonant energy exchange theory.
