An integrable model possessing inhomogeneous ground states is proposed as aneffective model of non-uniform quantum condensates such as supersolids andFulde--Ferrell--Larkin--Ovchinnikov superfluids. The model is a higher-orderanalog of the nonlinear Schr\"odinger equation. We derive an $n$-solitonsolution 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 exactbosonic and fermionic quasiparticle eigenstates and clarify their tunnelingphenomena. The solutions are expressed by a determinant of theta functions.
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机译：提出了一种具有不均匀基态的可积模型，作为超均匀固体和Fulde-Ferrell-Larkin-Ovchinnikov超流体等非均匀量子凝聚的有效模型。该模型是非线性Schr“ odinger方程的高阶模拟。我们通过具有椭圆函数背景的逆散射理论，导出了$ n $-孤子解，并揭示了各种孤子动力学，例如暗孤子台球，位错，灰色孤子和包络孤子。我们还提供了精确的正弦波和费米子准粒子本征态，并阐明了它们的隧穿现象，这些解由theta函数的决定子表示。
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