Multiple equilibrium states in pure-quartic soliton molecules

In this Letter, we demonstrate the existence of multiple equilibrium states in pure-quartic soliton (PQS) molecules. A discrete sequence of equilibrium separations alternating between stable and unstable states is theoretically predicted and numerically identified in the PQS doublet and triplet states. Furthermore, a systematic family tree of stable bound PQSs is constructed to facilitate the understanding of a hierarchical structure of stationary PQS molecules, thus allowing for the on-demand mixture of arbitrary orders of equilibrium separations and relative phase (in- or anti-phase) between adjacent PQSs. As typical examples, stable evolutions of the constructed four- and five-PQS molecules over distances are validated by the numerical simulations. These results can broaden the fundamental understanding of the interaction between PQSs and the intrinsic dynamics of PQS molecules, which also provides an avenue to manipulate the optical soliton compounds (macromolecules, crystals, etc.) in nonlinear optics.