Breather-breather interactions in sine-Gordon systems using collective coordinate approach.
Breather-breather interactions in sine-Gordon systems using collective coordinate approach.
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DOI：
10.1103/physreve.80.036603
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
M. Nishida;Yoshiki Furukawa;T. Fujii;N. Hatakenaka
中科院分区：
文献类型：
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作者：
M. Nishida;Yoshiki Furukawa;T. Fujii;N. Hatakenaka
我们使用集体坐标的方法研究sine-Gordon系统中呼吸子之间的相互作用。针对两个相同呼吸子的同相或异相振荡模式，我们导出了一个简单的集体坐标常微分方程：两个呼吸子的质心间距R。该方程的解析解可以在整个参数范围内定量地再现sine-Gordon方程的直接数值模拟结果。对于同相（异相）振荡模式，两个呼吸子之间的相互作用是吸引（排斥）的，对R具有渐近指数依赖性。我们发现，在最里面的扭结反扭结（扭结扭结）对同相（异相）的情况下，在确定有效的呼吸呼吸相互作用的符号和强度的相互作用中起着最重要的作用。我们还发现了同相振荡呼吸子对的内振荡模式，并得到了该模式角频率的解析表达式。
We investigate the interaction between breathers in sine-Gordon systems using a collective coordinate approach. Focusing on the in-phase or out-of-phase oscillation mode of two identical breathers, we derive a simple ordinary differential equation for the collective coordinate: the separation between the centers of mass of the two breathers R. Analytic solutions of this equation can reproduce quantitatively the results of a direct numerical simulation of the sine-Gordon equation over the whole parameter range. The interaction between the two breathers is attractive (repulsive) for the in-phase (out-of-phase) oscillation mode with an asymptotic exponential dependence on R. We find that the interaction within the innermost kink-antikink (kink-kink) pair for the in-phase (out-of-phase) case plays the most significant role in determining the sign and the strength of the effective breather-breather interaction. We also find an internal oscillation mode of the in-phase oscillating breather pair and obtain an analytic expression for the angular frequency of the mode.