AI 中文总结
研究复正弦-戈登模型中复扭结-扭结碰撞，通过数值研究确定最终状态与初始速度和相对相位的关系，揭示双临界速度分支及丰富的速度-相位依赖性，计算相关能量等并发现其在临界点的转变，表明相对相位在碰撞动力学中起重要作用。
AI 中文摘要
复正弦-戈登（CSG）模型包含一个内部相位自由度，它极大地改变了其孤波解的动力学。我们对复扭结-扭结碰撞进行了数值研究，并确定了最终状态如何共同取决于初始速度和相对相位。与实正弦-戈登模型的弹性碰撞不同，CSG系统呈现出散射、捕获、长寿命双离子形成、类呼吸状态以及辐射轮廓发射。模拟揭示了两个不同的与相位相关的临界速度分支。在一个分支中，增加初始速度促进捕获，而在另一个分支中则恢复散射。这种双重结构突出了碰撞动力学丰富的速度-相位依赖性。我们还计算了辐射轮廓携带的能量，并研究了碰撞中心处能量密度、动能和梯度贡献以及场模量的极值。这些量在临界点处显示出急剧转变，并为相位控制动力学提供了灵敏的诊断。这些结果表明相对相位表现为一个有效的内部自由度，在复孤子的碰撞动力学中起着重要作用。
英文摘要
The complex sine-Gordon (CSG) model contains an internal phase degree of freedom that strongly modifies the dynamics of its solitary-wave solutions. We present a numerical study of complex kink--kink collisions and determine how the final state depends jointly on the initial velocity and relative phase. In contrast with the elastic collisions of the real sine-Gordon model, the CSG system exhibits scattering, capture, long-lived bion formation, breather-like states, and emission of radiative profiles. The simulations reveal two distinct phase-dependent branches of critical velocity. In one branch, increasing the initial velocity promotes capture, whereas in the other it restores scattering. This dual structure highlights the rich velocity--phase dependence of the collision dynamics. We also compute the energy carried by radiative profiles and examine extreme values of the energy density, kinetic and gradient contributions, and field modulus at the collision center. These quantities show sharp transitions at critical points and provide sensitive diagnostics of phase-controlled dynamics. These results suggest that the relative phase behaves as an effective internal degree of freedom that plays an important role in the collision dynamics of complex solitons.
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