Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schrödinger equation

Abstract

We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing new mechanisms of decay of antidark solitons.

Bistable Helmholtz dark spatial optical solitons in materials with self-defocusing saturable nonlinearity

“…A bistability characteristic is also discussed. [17][18][19]22,23,27 Further analysis in Sec. 5 demonstrates that Helmholtz Kerr dark solitons 28 emerge from the new solutions in the limit that saturation effects are negligible (such an asymptotic result is a physical and mathematical requirement).…”

Wide vector solitons in systems with time- and space-modulated nonlinearities

“…Now, we consider the second solution of Eq. (38), that is, Detailed studies of the CQNLSE in both optics and BECs have been carried out in [35]. There, analytical soliton solutions are obtained and their stability and relation to dispersive shocks are analyzed.…”

Crossover dynamics of dispersive shocks in Bose-Einstein condensates characterized by two- and three-body interactions

“…(1), which has been thoroughly investigated recently [26]. Quite remarkably, although these solitons are mostly unstable [26], the average velocity v * of the DSW for x < 0 is such that the soliton (and hence the DSW) is totally stable on propagation. This can be rigorously demonstrated from the stability diagram of the antidark solitons of the cubicquintic nonlinear Schrödinger (CQNLS) equation (Fig.…”

“…The stability map is constructed by following the analysis of Ref. [26]. As seen, the numerically calculated velocity v * of the antidark soliton of Fig.…”

“…Zero-velocity antidark solitons of Eq. (1) are always unstable [26], and they lead the BEC toward irreversible collapse near x = 0 [ Fig. 6(b)].…”