The modified Korteweg–de Vries–sine-Gordon (mKdV–sG) equation is one of the models describing few-cycle-pulse optical solitons beyond the slowly varying envelope approximation. By introducing the velocity resonance mechanism to multiple soliton/breather solutions, it is found that the mKdV–sG model possesses abundant soliton molecule (SM), breather molecule (BM) and breather–soliton molecule (BSM) structures. Every SM includes only two solitons, a BM can be constructed by arbitrary number of breathers and a BSM can be formed from one or two solitons and arbitrary number of breathers. Though the interactions among the separated solitons and breathers are elastic, the size (the distances among solitons in a same molecule) will be changed after the interaction. Prospects of the studies overviewed in this work are given in the conclusions.

修正的Korteweg-de Vries-sine-Gordon（mKdV-sG）方程是描述超出缓变包络近似的几个周期脉冲光学孤子的模型之一。通过将速度共振机制引入多个孤子/呼吸解，发现mKdV–sG模型具有丰富的孤子分子（SM），通气分子（BM）和通气-孤子分子（BSM）结构。每个SM仅包含两个孤子，一个BM可以由任意数量的呼吸器构成，而BSM可以由一个或两个孤子和任意数量的呼吸器形成。尽管分离的孤子和呼吸器之间的相互作用是弹性的，但相互作用后大小（同一分子中的孤子之间的距离）将发生变化。结论中给出了这项工作概述的研究前景。