Purely Kerr nonlinear model admitting flat-top solitons

Surface gap solitons in the Schrödinger equation with quintic nonlinearity and a lattice potential

We demonstrate the existence of surface gap solitons, a special type of asymmetric solitons, in the one-dimensional nonlinear Schrödinger equation with quintic nonlinearity and a periodic linear potential. The nonlinearity is suddenly switched in a step-like fashion in the middle of the transverse spatial region, while the periodic linear potential is chosen in the form of a simple sin 2 lattice. The asymmetric nonlinearities in this work can be realized by the Feshbach resonance in Bose-Einstein condensates or by the photorefractive effect in optics. The major peaks in the gap soliton families are asymmetric and they are located at the position of the jump in nonlinearity (at x = 0). In addition, the major peaks of the two-peak and multi-peak solitons at the position x = 0 are higher than those after that position, at x > 0. And such phenomena are more obvious when the value of chemical potential is large, or when the difference of nonlinearity values across the jump is big. Along the way, linear stability analysis of the surface gap solitons is performed and the stability domains are identified. It is found that in this model, the solitons in the first band gap are mostly stable (excepting narrow domains of instability at the edges of the gap), while those in the second band gap are mostly unstable (excepting extremely narrow domains of stability for fundamental solitons). These findings are also corroborated by direct numerical simulations.

Triangular bright solitons in nonlinear optics and Bose-Einstein condensates

We demonstrate what we believe to be novel triangular bright solitons that can be supported by the nonlinear Schrödinger equation with inhomogeneous Kerr-like nonlinearity and external harmonic potential, which can be realized in nonlinear optics and Bose-Einstein condensates. The profiles of these solitons are quite different from the common Gaussian or sech envelope beams, as their tops and bottoms are similar to the triangle and inverted triangle functions, respectively. The self-defocusing nonlinearity gives rise to the triangle-up solitons, while the self-focusing nonlinearity supports the triangle-down solitons. Here, we restrict our attention only to the lowest-order fundamental triangular solitons. All such solitons are stable, which is demonstrated by the linear stability analysis and also clarified by direct numerical simulations. In addition, the modulated propagation of both types of triangular solitons, with the modulated parameter being the strength of nonlinearity, is also presented. We find that such propagation is strongly affected by the form of the modulation of the nonlinearity. For example, the sudden change of the modulated parameter causes instabilities in the solitons, whereas the gradual variation generates stable solitons. Also, a periodic variation of the parameter causes the regular oscillation of solitons, with the same period. Interestingly, the triangle-up and triangle-down solitons can change into each other, when the parameter changes the sign.

Dark soliton families in quintic nonlinear lattices

We prove that the dark solitons can be stable in the purely quintic nonlinear lattices, including the fundamental, tripole and five-pole solitons. These dark soliton families are generated on the periodic nonlinear backgrounds. The propagation constant affects the forms of these solitons, while the number of poles does not lead to the variation of the backgrounds. The dark solitons are stable only when the propagation constant is moderately large.