Darker-than-black solitons: Dark solitons with total phase shift greater than pi

Modulational instability in nonlinear saturable media with competing nonlocal nonlinearity

The modulational instability (MI) phenomenon is addressed in a nonlocal medium under controllable saturation. The linear stability analysis of a plane-wave solution is used to derive an expression for the growth rate of MI that is exploited to parametrically discuss the possibility for the plane wave to disintegrate into nonlinear localized light patterns. The influence of the nonlocal parameter, the saturation coefficient, and the saturation index are mainly explored in the context of a Gaussian nonlocal response. It is pointed out that the instability spectrum, which tends to be quenched by the high nonlocality parameter, gets amplified under the right choices of the saturation parameters, especially the saturation index. Via direct numerical simulations, confirmations of analytical predictions are given, where competing nonlocal and saturable nonlinearities enable the emergence of trains of patterns as manifestations of MI. The comprehensive parametric analysis carried out throughout the numerical experiment reveals the robustness of the obtained rogue waves of A- and B-type Akhmediev breathers, as the nonlinear signature of MI, providing the saturation index as a suitable tool to manipulate nonlinear waves in nonlocal media.

Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions

We obtain multivalley dark soliton solutions with asymmetric or symmetric profiles in multicomponent repulsive Bose-Einstein condensates by developing the Darboux transformation method. We demonstrate that the width-dependent parameters of solitons significantly affect the velocity ranges and phase jump regions of multivalley dark solitons, in sharp contrast to scalar dark solitons. For double-valley dark solitons, we find that the phase jump is in the range [0,2π], which is quite different from that of the usual single-valley dark soliton. Based on our results, we argue that the phase jump of an n-valley dark soliton could be in the range [0,nπ], supported by our analysis extending up to five-component condensates. The interaction between a double-valley dark soliton and a single-valley dark soliton is further investigated, and we reveal a striking collision process in which the double-valley dark soliton is transformed into a breather after colliding with the single-valley dark soliton. Our analyses suggest that this breather transition exists widely in the collision processes involving multivalley dark solitons. The possibilities for observing these multivalley dark solitons in related Bose-Einstein condensates experiments are discussed.

Classification of dark solitons via topological vector potentials

Dark solitons are some of the most interesting nonlinear excitations and are considered to be the one-dimensional topological analogs of vortices. However, in contrast to their two-dimensional vortex counterparts, the topological characteristics of a dark soliton are far from fully understood because the topological charge defined according to the phase jump cannot reflect its essential property. Here, similar to the complex extension used in the exploration of the partition-function zeros to depict thermodynamic states, we extend the complex coordinate space to explore the density zeros of dark solitons. Surprisingly we find that these zeros constitute some pointlike magnetic fields, each of which has a quantized magnetic flux of elementary π. The corresponding vector potential fields demonstrate the topology of the Wess-Zumino term and can depict the essential characteristics of dark solitons. Then we classify the dark solitons according to the Euler characteristic of the topological manifold of the vector potential fields. Our study not only reveals the topological features of dark solitons but can also be applied to explore and identify new dark solitons with high topological complexity.

Drag force in bimodal cubic-quintic nonlinear Schrödinger equation

We consider a system of two cubic-quintic nonlinear Schrödinger equations in two dimensions, coupled by repulsive cubic terms. We analyze situations in which a probe lump of one of the modes is surrounded by a fluid of the other one and analyze their interaction. We find a realization of D'Alembert's paradox for small velocities and nontrivial drag forces for larger ones. We present numerical analysis including the search of static and traveling form-preserving solutions along with simulations of the dynamical evolution in some representative examples.

Ring dark solitary waves: experiment versus theory

Experimental results on optical ring dark solitary wave dynamics are presented, emphasizing the interplay between initial dark beam contrast, total phase shift, background-beam intensity, and saturation of the nonlinearity. The results are found to confirm qualitatively the existing analytical theory and are in agreement with the numerical simulations carried out.

Solitons in nonlocal nonlinear media: exact solutions

We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties of these solitons and show their stability.

Modulational instability of multiple-charged optical vortex solitons under saturation of the nonlinearity

We present a linear analysis and numerical simulations of the instability of optical vortex solitons (OVSs) of arbitrary topological charge. They show a rich variety of instability scenarios depending on the type of perturbation. The saturation of the nonlinearity is shown to be able to slow down the decay of multiple charged dark beams at an intermediate evolution stage and to prevent their ultimate decay into charge-1 OVSs. This concept is experimentally verified by the observation of a partial decay of a triple-charged OV beam and by comparing this dynamic with the behavior of OV beams of topological charges m=1, 2, 3, and 4.

Hamiltonian-versus-energy diagrams in soliton theory

Parametric curves featuring Hamiltonian versus energy are useful in the theory of solitons in conservative nonintegrable systems with local nonlinearities. These curves can be constructed in various ways. We show here that it is possible to find the Hamiltonian (H) and energy (Q) for solitons of non-Kerr-law media with local nonlinearities without specific knowledge of the functional form of the soliton itself. More importantly, we show that the stability criterion for solitons can be formulated in terms of H and Q only. This allows us to derive all the essential properties of solitons based only on the concavity of the curve H vs Q. We give examples of these curves for various nonlinearity laws and show that they confirm the general principle. We also show that solitons of an unstable branch can transform into solitons of a stable branch by emitting small amplitude waves. As a result, we show that simple dynamics like the transformation of a soliton of an unstable branch into a soliton of a stable branch can also be predicted from the H-Q diagram.

Stability of black solitons in media with arbitrary nonlinearity

It is shown that the black solitons in an optical fiber or a uniform medium with arbitrary nonlinearity are all stable. The conclusion from the analytical stability analysis is consistent with that of numerical simulations. This then dismisses a previous criterion that suggests that the black solitons in a saturable nonlinear medium can be unstable.

Instabilities of dark solitons

Optical dark solitons described by the generalized nonlinear Schrödinger equation are discussed, and the criterion of soliton instability is presented. This analytical criterion is confirmed numerically for an exactly solvable model of nonlinear saturation.