Under investigation in this article is a multi-component AB system which models the self-induced transparency phenomenon. By using the modified Darboux transformation, we present the breather solutions of such system. We study the subtle mechanism that converts the breathing state into the solitary and periodic ones, through which we obtain various stationary nonlinear excitations such as the multi-peak solitons, (quasi) periodic waves, (quasi) anti-dark solitons, W-shaped solitons and M-shaped solitons which exhibit stationary feature. According to the analysis of the group velocity difference, we give the corresponding conversion rule and present the explicit correspondence of phase diagram of wave numbers for various converted waves, by which we show the gradient relation among these converted waves. Further, by separating the converted waves into the solitary wave as well as the periodic wave, we classify different kinds of nonlinear waves and indicate the difference of the superposition mechanism among them. We show that the breather and various converted waves are formed by different superposition modes between the solitary wave components with different localities and periodic wave components with different frequencies. By virtue of the second-order solutions, we consider all possible superposition situations of two nonlinear waves and present the corresponding nonlinear wave complexes. In particular, for the hybrid structure made of a breather and a nonlinear wave with variable velocity, we then discover that the nonlinear wave does not change its state under the conversion condition, leading to that an additional breathing structure or a dark structure is contained in the converted waves. Finally, we unveil the underlying relationship between the conversion and modulation instability.

本文正在研究的是一种多组分AB系统，该系统可以模拟自感应的透明现象。通过使用改进的Darboux变换，我们提出了这种系统的通气解决方案。我们研究了将呼吸状态转换为孤立状态和周期性状态的微妙机理，通过这种机理我们获得了各种平稳的非线性激励，例如多峰孤子，（准）周期波，（准）反暗孤子，W形孤子和M形孤子具有固定特征。通过对群速度差的分析，给出了相应的转换规则，并给出了各种转换波的波数相位图的显式对应关系，从而表明了这些转换波之间的梯度关系。进一步，通过将转换后的波分为孤立波和周期波，我们对不同种类的非线性波进行了分类，并指出了它们之间叠加机制的差异。我们表明通气孔和各种转换波是由不同位置的孤立波分量和不同频率的周期波分量之间的不同叠加模式形成的。借助二阶解，我们考虑了两个非线性波的所有可能叠加情况，并给出了相应的非线性波复合体。特别是，对于由通气管和速度可变的非线性波组成的混合结构，我们发现非线性波在转换条件下不会改变其状态，导致转换后的波中包含额外的呼吸结构或深色结构。最后，我们揭示了转换和调制不稳定性之间的潜在关系。