Dynamics of Controllable Matter-Wave Solitons and Soliton Molecules for a Rabi-Coupled Gross–Pitaevskii Equation with Temporally and Spatially Modulated Coefficients

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 1, Page 748-778, March 2024.
Abstract. This paper studies the soliton dynamics for the Rabi-coupled Gross–Pitaevskii model in multicomponent Bose–Einstein condensates. The model has variable nonlinearities and external potentials and is used to construct a complex multisoliton in an explicit form. The variable nonlinearity and external potential cause the soliton to compress and change its velocity, respectively. A new generalized similarity transformation is proposed to eliminate the [math] Rabi-coupled terms in the [math]-component model, which can make the Hirota bilinear method be applied to obtain multisoliton solutions. The bound state of the two-soliton forms the soliton molecule under velocity resonance. Asymptotic analysis can give the asymptotic expressions of each single soliton in multisoliton solutions, which can clearly give each soliton’s width, velocity, amplitude, and energy; these parameters can control multisolitons. When the solitons’ relative velocity or the solitons’ width is large, the interferogram between solitons will be observed. Numerical simulation shows that these solitons can steadily propagate. It is easy for the soliton molecule and interference dynamics to occur because of the controlled soliton. Since the coupled Gross–Pitaevskii equation describes the mechanics of matter waves in Bose–Einstein condensates, it is proved that we can observe the stable solitons and soliton molecules in Bose–Einstein condensates. The method and results presented in this paper are also common to other similar models. When observing particle multiple distributions, quantum interferometry, and interferometers, the results presented and the model in this paper can provide a reference for these applications.