Fig. 1. (a) Stable soliton solution in Eq. (1). (b) Soliton dynamics for various sharpnesses (from top to bottom: n=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9) of the elliptical shaped potential when p=3 for M=2 and N=5. The transverse domain is (−50,50)×(−50,50).

Fig. 2. Regions of different soliton dynamics in the plane (n, p) when M=2 and N=5. In region A, for soliton localization; in region B, for soliton straight-line arrays; in regions C and D, for soliton evolution into one elliptical ring soliton array and a set of elliptical ring solitons, respectively; in region E, for soliton decay.

Fig. 3. Soliton dynamics for various sharpnesses (top: n=0.5, middle: n=0.6, bottom: n=0.7) of the elliptical shaped potential when p=3 for M=3 and (a) N=5; (b) N=6; (c) N=7; (d) N=8. The transverse domain is (−60,60)×(−60,60).

Fig. 4. Regions of dynamic regimes in the plane (M, N) when p=3 and n=0.6.

Fig. 5. Soliton dynamics for various sharpnesses n = (a) 0.5, (b) 0.6, and (c) 0.7 of the tapered-elliptical potential when p=1 for M=2 and N=5. The transverse domain is (−60,60)×(−60,60).