Weakly bound solitons and two-soliton molecules in dipolar Bose–Einstein condensates

Abstract

Analytic expressions have been derived for the interaction potential between dipolar bright solitons and the binding energy of a two-soliton molecule. The properties of these localized structures are explored with a focus on their behavior in the weakly bound regime, with a small binding energy. Using the variational approach a coupled system of ordinary differential equations for the parameters of a soliton molecule is obtained for the description of their evolution. Predictions of the model are compared with numerical simulations of the governing nonlocal Gross-Pitaevskii equation and good qualitative agreement between them is demonstrated.

Novel soliton molecules and wave interactions for a (3 + 1)-dimensional nonlinear evolution equation

“…Recently, soliton molecules have attracted much attention for their continuous discoveries in nonlinear optical experiments [19][20][21][22]. As a special type of nonlinear excitations, soliton molecules have also been demonstrated in other physical systems, such as in dipolar Bose-Einstein condensates [23]. Soliton molecules come along from some fundamental solitons acting as "atoms" [24].…”

Oscillations of a quasi-one-dimensional dipolar supersolid

“…A new kind of dipolar quantum droplets, which can be made of strongly interacting bosons, was reported in [17]. In the strongly interacting Tonks-Girardeau regime, the governing equation of reference [17] reduces to the nonlocal Gross-Pitaevskii equation (GPE) with quintic nonlinearity, previously studied in the context of flat-top localized states in quasi-1D dipolar condensates [18,19], while in the weakly interacting limit it reduces to usual nonlocal GPE with cubic nonlinearity [20,21]. In a recent study [22], the authors have derived the modified GPE, taking into account the next order (beyond LHY) quantum fluctuation effects.…”