FIG. 8.14 The left and right panels display experimentally observed transverse (spatial) and longitudinal (temporal) structure of the fundamental spatiotemporal quasi-soliton created in the multi-core waveguide, whose cross-section structure is shown in Fig. 8.12 ( Minardi et al., 2010 ). More about this image found in The left and right panels display experimentally observed transverse (spati...

FIG. 13.1 A scheme for the creation of quasi-2D (“pancake-shaped”) solitons supported by the DDI between magnetic atoms confined in the vertical direction by the HO trapping potential. The angle between the fixed orientation of atomic magnetic dipoles, p ^ , and the confinement direction is θ ( Chen et al., 2017 ). More about this image found in A scheme for the creation of quasi-2D (“pancake-shaped”) solitons supported...

FIG. 14.45 Plots of |U(x, y, t, z)| in the plane of x = y = 0 illustrate typical outcomes of collisions between two 3D dissipative vortex solitons with S = 2, produced by simulations of Eq. (5.64) with parameters ( 14.66 ) and initial conditions ( 14.65 ). (a) Merger of the slowly colliding solitons, which were set in motion by the kicks with χ = 0.5 (see the detailed picture in Fig. 14.46 ). (b) Creation of an additional quiescent soliton with S = 2 in the case of χ = 2 . (c) Quasi-elastic collision of fast solitons in the case of χ = 4 , see the detailed picture in Fig. 14.47 ( Mihalache et al., 2008a ). More about this image found in Plots of |U(x, y,

FIG. 13.2 The left panel: the density distribution produced by a stable quasi-2D (pancake-shaped) soliton solution of Eq. ( 13.12 ) in the mid plane, y = 0, for parameters g = 10 and g/g_DDI = 0.911 [which satisfies the necessary condition ( 13.23 )]. The right panel: the same, as predicted by the VA solution based on Ansatz ( 13.14 ) ( Tikhonenkov et al., 2008a ). More about this image found in The left panel: the density distribution produced by a stable quasi-2D (pan...

FIG. 1.16 Left: The experimentally observed density distribution in a quasi-stable TS (Townes soliton) created in a minority component of a binary condensate of ⁸⁷Rb atoms, embedded in the majority background. The effective self-attraction in the minority component, which is necessary to build the TS, is induced by the immiscibility of the binary system. Right: The experimentally observed radial profile of the same TS (the chain of dots), fitted to the respective numerical solution of Eq. ( 1.103 ). The inset shows the same data on the semilog scale, highlighting the exponentially decaying structure of the TS’s tails ( Bakkali-Hassani et al., 2021 ). More about this image found in Left: The experimentally observed density distribution in a quasi-stable TS...

FIG. 4.1 The left panel displays a set of experimentally recorded (at different propagation distances z, as indicated in the figure) power-density profiles of a vortex light beam, with winding number S = 1, which propagates through the nonlinear optical material (carbon disulfide). Plot (a) was obtained for a low value of the initial power density, 1 GW/cm², which corresponds to the linear propagation regime. It shows diffractive spread-out of the vortex ring, as designated by dashed yellow lines. Plot (b) represents an essentially nonlinear regime corresponding to an initial power density of 9 GW/cm². In the latter case, a quasi-stable vortex soliton is observed, as stressed by means of solid green lines. In the right panel, columns (a) and (b) show counterparts of the same propagation regimes produced by simulations of Eq. ( 4.1 ), with a physically relevant value of the three-photon-absorption coefficient γ . In addition, columns (c) and (d) display results of the simulations for still higher initial power densities, viz., 12 and 15 GW/cm², in which case the nonlinear vortex beam is subject to the splitting instability ( Reyna et al., 2016 ). More about this image found in The left panel displays a set of experimentally recorded (at different prop...