Integrable model for density-modulated quantum condensates: solitons passing through a soliton lattice

Understand

An integrable model possessing inhomogeneous ground states is proposed as an effective model of non-uniform quantum condensates such as supersolids and Fulde--Ferrell--Larkin--Ovchinnikov superfluids.

• The model is a higher-order analog of the nonlinear Schr\"odinger equation.
• We derive an $n$-soliton solution via the inverse scattering theory with elliptic-functional background, and reveal various kinds of soliton dynamics such as dark soliton billiards, dislocations, gray solitons, and envelope solitons.
• We also provide the exact bosonic and fermionic quasiparticle eigenstates and clarify their tunneling phenomena.