Abstract
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.
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