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Finally, we note that a very related problem in the field of Bose-Einstein condensates is the stabilization of multidimensional matter-wave solitons, which dynamics can be described by the discrete GrossPitaevskii equation which is mathematically equivalent to Eq. (1). Several methods of stabilization have been considered to date. Discreteness can be introduced by applying deep opti- cal lattices, with the cost of reducing the soliton mo- bility to one dimension [4]. On the other hand, shal- 

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## IV. MATTER-WAVE SOLITONS 

low optical lattices can be used to manipulate the effec- tive mass of the mater waves [38–40], allowing for sta- bilization of dispersion-managed solitons in two dimen- sions [41]. Stabilization of subdiffractive solitons with almost zero dispersion in lattices in two dimensions was also proposed [13]. Another approach consists of modula- tion of the nonlinear coupling using Feshbach resonances. In this context, stable two dimensional solitons were pre- dicted [42–44], however stabilization in the full three- dimensional case requires an additional potential [45–47], feedback control of the nonlinearity [48] or inclusion of inelastic losses [49]. Nonlocal dipolar interactions were also shown to provide stabilization of quasi two dimen- sional BEC solitons [50, 51]. 

Our method can provide an alternative solution to the stabilization of matter-wave solitons. We estimate that in the case of a Bose-Einstein condensate of $^{7}$Li atoms in the quasi two dimensional setting with the axial trapping frequency ω$_{⊥}$ = 2 π × 300 Hz, the lattice constant has the value d = λ/ 2 = 0 . 4 µ m, the width along the lattice axis W$_{x}$ = 6 . 5 µ m, transverse width W$_{y}$ = 20 . 9 µ m and the number of atoms N = 4000, where we assumed that the scattering length is tuned to a$_{s}$ = − 5 a$_{0}$ using a Feschbach resonance [52]. The time period of the lattice modulation is equal to τ = 45 ms and the total time of evolution in Fig. 2(a) is 0 . 7 s. 

We have demonstrated that arrays of curved waveg- uides can be used to stabilize two- and three-dimensional light bullets against the collapse in media with Kerr-type nonlinearity. Most remarkably, the bullets can freely move across the periodic structure, unlike the previously considered discrete light bullets which were trapped to a specific lattice site. These results suggest new possibil- ities for flexible spatio-temporal manipulation of optical pulses, and they are also relevant for the stabilization of multidimensional matter-wave solitons. 

This work was supported by the Australian Research Council. 

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## V. CONCLUSIONS 

