Vectorial Dark–Bright Solitons: Dynamics & Stability

• Vectorial dark–bright solitons are composite solitary waves in coupled nonlinear fields, where a dark dip on a continuous background traps a bright localized hump.
• They manifest in diverse settings such as Bose–Einstein condensates, nonlinear optical media, and metamaterials, demonstrating unique intercomponent trapping dynamics.
• Analytical, traveling-wave, and variational approaches reveal their stability properties and rich dynamical behaviors beyond mean-field approximations.

Searching arXiv for recent and foundational papers on vectorial dark-bright solitons. Vectorial dark–bright solitons are composite solitary waves in coupled nonlinear field systems in which one component carries a dark structure on a nonzero background while a second component forms a bright localized hump on a vanishing background. In the one-dimensional defocusing Gross–Pitaevskii setting, they arise as traveling waves of two coupled complex fields with asymptotics $|\Psi(x,t)|\to 1$ and $|\Phi(x,t)|\to 0$ as $|x|\to\infty$, so that the first component is “dark” and the second “bright” (López-Martínez, 26 Aug 2025). The same structural motif appears in mixtures of Bose–Einstein condensates, nonlinear optical media, waveguide arrays, nematic liquid crystals, chiral metamaterials, and driven cavities, where cross-phase coupling allows a bright excitation to be trapped by the density notch of a dark component rather than by self-focusing alone (Arazo et al., 2021).

1. Governing equations and defining structure

A canonical model is the coupled one-dimensional defocusing Gross–Pitaevskii system

$$\begin{cases} i\,\partial_t\Psi = \partial_{xx}\Psi + \bigl(1-|\Psi|^2-\alpha |\Phi|^2\bigr)\Psi,\ i\,\partial_t\Phi = \partial_{xx}\Phi - \bigl(\alpha |\Psi|^2+\beta |\Phi|^2\bigr)\Phi, \end{cases} \qquad (x,t)\in\mathbb R^2,$$

with $\alpha>0$, $\beta\ge 0$, together with the physically imposed boundary conditions

$$|\Psi(x,t)|\to 1,\qquad |\Phi(x,t)|\to 0 \qquad \text{as } |x|\to\infty .$$

In this formulation, the dark component is the field with nonzero asymptotic modulus, and the bright component is the field that decays spatially (López-Martínez, 26 Aug 2025).

For trapped two-component Bose–Einstein condensates, a widely used quasi-one-dimensional model is

$$i\,\partial_t\psi_i = \left[ -\tfrac12 \partial_x^2+\tfrac12 x^2+g_{ii}|\psi_i|^2+g_{12}|\psi_j|^2 \right]\psi_i, \qquad i\neq j\in\{1,2\},$$

with repulsive intraspecies and interspecies interactions. In immiscible mixtures, phase separation requires $g_{12}>\sqrt{g_{11}g_{22}}=g$, and equilibrium supports two spatial domains separated by a smooth interface or domain wall (Arazo et al., 2021).

The defining mechanism is intrinsically vectorial. The dark component’s density dip provides an effective potential well that traps the bright component, which by itself could not self-confine under repulsive interactions. Conversely, the trapped bright atoms increase the inertia of the dark hole and modify its phase-profile dynamics (Arazo et al., 2021). This mutual trapping distinguishes dark–bright solitons from scalar dark or bright solitary waves.

2. Traveling-wave reductions and analytic solution families

A standard traveling-wave ansatz for the defocusing Gross–Pitaevskii system is

$$\Psi(x,t)=u(\xi),\qquad \Phi(x,t)=e^{\,i\bigl((\lambda+\tfrac{c^2}{4})t-\tfrac{c}{2}x\bigr)}\,v(\xi), \qquad \xi=x-ct,$$

with $|\Phi(x,t)|\to 0$0, where $|\Phi(x,t)|\to 0$1 can be taken real. Writing $|\Phi(x,t)|\to 0$2, the profile equations become

$|\Phi(x,t)|\to 0$3

subject to $|\Phi(x,t)|\to 0$4 and $|\Phi(x,t)|\to 0$5 as $|\Phi(x,t)|\to 0$6 (López-Martínez, 26 Aug 2025).

In the Manakov case $|\Phi(x,t)|\to 0$7 with equal chemical potentials and $|\Phi(x,t)|\to 0$8, an explicit dark–bright profile on a uniform background density $|\Phi(x,t)|\to 0$9 is

$|x|\to\infty$0

$|x|\to\infty$1

with inverse width

$|x|\to\infty$2

bright amplitude

$|x|\to\infty$3

and bright mass

$|x|\to\infty$4

Localization demands $|x|\to\infty$5 and real $|x|\to\infty$6 (Arazo et al., 2021).

In homogeneous one-dimensional settings, an exact dark–bright ansatz can also be written as

$|x|\to\infty$7

$|x|\to\infty$8

with

$|x|\to\infty$9

Here the bright-component atom number $$\begin{cases} i\,\partial_t\Psi = \partial_{xx}\Psi + \bigl(1-|\Psi|^2-\alpha |\Phi|^2\bigr)\Psi,\ i\,\partial_t\Phi = \partial_{xx}\Phi - \bigl(\alpha |\Psi|^2+\beta |\Phi|^2\bigr)\Phi, \end{cases} \qquad (x,t)\in\mathbb R^2,$$0 sets the amplitude, while the dark component provides the trapping notch (Middelkamp et al., 2010).

The family of known analytic solutions is broader than the equal-width Manakov class. For coupled nonlinear Schrödinger equations with unequal dispersion coefficients, the bright component satisfies a linearized Pöschl–Teller eigenvalue problem in the effective well generated by the dark component, and the $$\begin{cases} i\,\partial_t\Psi = \partial_{xx}\Psi + \bigl(1-|\Psi|^2-\alpha |\Phi|^2\bigr)\Psi,\ i\,\partial_t\Phi = \partial_{xx}\Phi - \bigl(\alpha |\Psi|^2+\beta |\Phi|^2\bigr)\Phi, \end{cases} \qquad (x,t)\in\mathbb R^2,$$1th bound state exists when

$$\begin{cases} i\,\partial_t\Psi = \partial_{xx}\Psi + \bigl(1-|\Psi|^2-\alpha |\Phi|^2\bigr)\Psi,\ i\,\partial_t\Phi = \partial_{xx}\Phi - \bigl(\alpha |\Psi|^2+\beta |\Phi|^2\bigr)\Phi, \end{cases} \qquad (x,t)\in\mathbb R^2,$$2

so that ground and excited bright states bifurcate at explicit thresholds (Charalampidis et al., 2014). Likewise, a later analytical family allows strikingly different inverse widths $$\begin{cases} i\,\partial_t\Psi = \partial_{xx}\Psi + \bigl(1-|\Psi|^2-\alpha |\Phi|^2\bigr)\Psi,\ i\,\partial_t\Phi = \partial_{xx}\Phi - \bigl(\alpha |\Psi|^2+\beta |\Phi|^2\bigr)\Phi, \end{cases} \qquad (x,t)\in\mathbb R^2,$$3 and $$\begin{cases} i\,\partial_t\Psi = \partial_{xx}\Psi + \bigl(1-|\Psi|^2-\alpha |\Phi|^2\bigr)\Psi,\ i\,\partial_t\Phi = \partial_{xx}\Phi - \bigl(\alpha |\Psi|^2+\beta |\Phi|^2\bigr)\Phi, \end{cases} \qquad (x,t)\in\mathbb R^2,$$4,

$$\begin{cases} i\,\partial_t\Psi = \partial_{xx}\Psi + \bigl(1-|\Psi|^2-\alpha |\Phi|^2\bigr)\Psi,\ i\,\partial_t\Phi = \partial_{xx}\Phi - \bigl(\alpha |\Psi|^2+\beta |\Phi|^2\bigr)\Phi, \end{cases} \qquad (x,t)\in\mathbb R^2,$$5

$$\begin{cases} i\,\partial_t\Psi = \partial_{xx}\Psi + \bigl(1-|\Psi|^2-\alpha |\Phi|^2\bigr)\Psi,\ i\,\partial_t\Phi = \partial_{xx}\Phi - \bigl(\alpha |\Psi|^2+\beta |\Phi|^2\bigr)\Phi, \end{cases} \qquad (x,t)\in\mathbb R^2,$$6

with width ratio $$\begin{cases} i\,\partial_t\Psi = \partial_{xx}\Psi + \bigl(1-|\Psi|^2-\alpha |\Phi|^2\bigr)\Psi,\ i\,\partial_t\Phi = \partial_{xx}\Phi - \bigl(\alpha |\Psi|^2+\beta |\Phi|^2\bigr)\Phi, \end{cases} \qquad (x,t)\in\mathbb R^2,$$7. In the integrable limit $$\begin{cases} i\,\partial_t\Psi = \partial_{xx}\Psi + \bigl(1-|\Psi|^2-\alpha |\Phi|^2\bigr)\Psi,\ i\,\partial_t\Phi = \partial_{xx}\Phi - \bigl(\alpha |\Psi|^2+\beta |\Phi|^2\bigr)\Phi, \end{cases} \qquad (x,t)\in\mathbb R^2,$$8, one finds $$\begin{cases} i\,\partial_t\Psi = \partial_{xx}\Psi + \bigl(1-|\Psi|^2-\alpha |\Phi|^2\bigr)\Psi,\ i\,\partial_t\Phi = \partial_{xx}\Phi - \bigl(\alpha |\Psi|^2+\beta |\Phi|^2\bigr)\Phi, \end{cases} \qquad (x,t)\in\mathbb R^2,$$9, but away from integrability $\alpha>0$0 may take any value in a wide interval, including $\alpha>0$1 in the reported examples (Mao et al., 2024). A common simplification in the literature is therefore only a special case, not a general property.

3. Variational characterization and rigorous existence

A rigorous existence theory for one-dimensional defocusing Gross–Pitaevskii dark–bright solitons is formulated in the energy space

$\alpha>0$2

with renormalized energy

$\alpha>0$3

The two constraints are the bright mass

$\alpha>0$4

and the dark modified momentum

$\alpha>0$5

where $\alpha>0$6 for $\alpha>0$7 (López-Martínez, 26 Aug 2025).

The constrained variational problem is

$\alpha>0$8

Its analysis proceeds through monotonicity in $\alpha>0$9, subadditivity, and strict energy decrease when $\beta\ge 0$0, followed by a rearrangement step using Hardy–Littlewood, Pólya–Szegő, and Garrisi’s strict estimate. Compactness of minimizing sequences is then obtained through concentration–compactness in the sense of Lions, where vanishing is excluded by a strict energy gap and dichotomy by strict subadditivity (López-Martínez, 26 Aug 2025).

The resulting minimizer is a constrained critical point solving the traveling-wave system. The Lagrange multiplier $\beta\ge 0$1 associated with the momentum constraint satisfies

$\beta\ge 0$2

and one has

$\beta\ge 0$3

which yields the subsonic speed condition $\beta\ge 0$4 (López-Martínez, 26 Aug 2025).

The minimizer can moreover be taken so that

$\beta\ge 0$5

and $\beta\ge 0$6 and $\beta\ge 0$7 are even in $\beta\ge 0$8 and nonincreasing in $\beta\ge 0$9. In particular, $$|\Psi(x,t)|\to 1,\qquad |\Phi(x,t)|\to 0 \qquad \text{as } |x|\to\infty .$$0 on $$|\Psi(x,t)|\to 1,\qquad |\Phi(x,t)|\to 0 \qquad \text{as } |x|\to\infty .$$1 and $$|\Psi(x,t)|\to 1,\qquad |\Phi(x,t)|\to 0 \qquad \text{as } |x|\to\infty .$$2, so the soliton pair consists of a strict dark notch and a strict bright bump. The rigorous outcome is a fully nontrivial dark–bright traveling wave with prescribed bright mass $$|\Psi(x,t)|\to 1,\qquad |\Phi(x,t)|\to 0 \qquad \text{as } |x|\to\infty .$$3, dark momentum $$|\Psi(x,t)|\to 1,\qquad |\Phi(x,t)|\to 0 \qquad \text{as } |x|\to\infty .$$4, and subsonic speed $$|\Psi(x,t)|\to 1,\qquad |\Phi(x,t)|\to 0 \qquad \text{as } |x|\to\infty .$$5 (López-Martínez, 26 Aug 2025).

4. Trapped dynamics, generation mechanisms, and interaction physics

In weak axial traps, dark–bright solitons behave as effective particles with an oscillation frequency identified with the anomalous mode of the Bogoliubov spectrum. A small-amplitude approximation gives

$$|\Psi(x,t)|\to 1,\qquad |\Phi(x,t)|\to 0 \qquad \text{as } |x|\to\infty .$$6

so that $$|\Psi(x,t)|\to 1,\qquad |\Phi(x,t)|\to 0 \qquad \text{as } |x|\to\infty .$$7 yields the scalar dark-soliton limit $$|\Psi(x,t)|\to 1,\qquad |\Phi(x,t)|\to 0 \qquad \text{as } |x|\to\infty .$$8, while increasing bright occupation lowers the oscillation frequency (Middelkamp et al., 2010). Experiments in an elongated optical dipole trap with $$|\Psi(x,t)|\to 1,\qquad |\Phi(x,t)|\to 0 \qquad \text{as } |x|\to\infty .$$9 reported $$i\,\partial_t\psi_i = \left[ -\tfrac12 \partial_x^2+\tfrac12 x^2+g_{ii}|\psi_i|^2+g_{12}|\psi_j|^2 \right]\psi_i, \qquad i\neq j\in\{1,2\},$$0 Hz for $$i\,\partial_t\psi_i = \left[ -\tfrac12 \partial_x^2+\tfrac12 x^2+g_{ii}|\psi_i|^2+g_{12}|\psi_j|^2 \right]\psi_i, \qquad i\neq j\in\{1,2\},$$1, $$i\,\partial_t\psi_i = \left[ -\tfrac12 \partial_x^2+\tfrac12 x^2+g_{ii}|\psi_i|^2+g_{12}|\psi_j|^2 \right]\psi_i, \qquad i\neq j\in\{1,2\},$$2, and $$i\,\partial_t\psi_i = \left[ -\tfrac12 \partial_x^2+\tfrac12 x^2+g_{ii}|\psi_i|^2+g_{12}|\psi_j|^2 \right]\psi_i, \qquad i\neq j\in\{1,2\},$$3 Hz for $$i\,\partial_t\psi_i = \left[ -\tfrac12 \partial_x^2+\tfrac12 x^2+g_{ii}|\psi_i|^2+g_{12}|\psi_j|^2 \right]\psi_i, \qquad i\neq j\in\{1,2\},$$4, $$i\,\partial_t\psi_i = \left[ -\tfrac12 \partial_x^2+\tfrac12 x^2+g_{ii}|\psi_i|^2+g_{12}|\psi_j|^2 \right]\psi_i, \qquad i\neq j\in\{1,2\},$$5, in qualitative agreement with the theoretical prediction that more bright atoms slow the oscillation (Middelkamp et al., 2010).

A distinct dynamical route appears in immiscible condensates. A dark soliton incident on a domain wall exhibits three numerically identified regimes: transmission for weak interspecies repulsion $$i\,\partial_t\psi_i = \left[ -\tfrac12 \partial_x^2+\tfrac12 x^2+g_{ii}|\psi_i|^2+g_{12}|\psi_j|^2 \right]\psi_i, \qquad i\neq j\in\{1,2\},$$6, wall-crossing with atom capture and DB generation for $$i\,\partial_t\psi_i = \left[ -\tfrac12 \partial_x^2+\tfrac12 x^2+g_{ii}|\psi_i|^2+g_{12}|\psi_j|^2 \right]\psi_i, \qquad i\neq j\in\{1,2\},$$7, and reflection with DB creation for $$i\,\partial_t\psi_i = \left[ -\tfrac12 \partial_x^2+\tfrac12 x^2+g_{ii}|\psi_i|^2+g_{12}|\psi_j|^2 \right]\psi_i, \qquad i\neq j\in\{1,2\},$$8. The resulting DB soliton oscillates harmonically inside its host component with a frequency $$i\,\partial_t\psi_i = \left[ -\tfrac12 \partial_x^2+\tfrac12 x^2+g_{ii}|\psi_i|^2+g_{12}|\psi_j|^2 \right]\psi_i, \qquad i\neq j\in\{1,2\},$$9, and the key qualitative result is that a fully nonlinear DB emerges dynamically for all $g_{12}>\sqrt{g_{11}g_{22}}=g$0, even outside the parameter window where stationary solutions are known analytically (Arazo et al., 2021). This directly limits the common assumption that stationary existence bounds exhaust the dynamical phenomenology.

Quench protocols across the miscible–immiscible threshold generate multiple DB structures through modulational instability and filamentation. For miscible $g_{12}>\sqrt{g_{11}g_{22}}=g$1 immiscible quenches, the DB count satisfies the reported scalings

$g_{12}>\sqrt{g_{11}g_{22}}=g$2

up to saturation near balance, and

$g_{12}>\sqrt{g_{11}g_{22}}=g$3

while tighter traps suppress production (Kiehn et al., 2019). In the reported quasi-one-dimensional simulations with $g_{12}>\sqrt{g_{11}g_{22}}=g$4, the same protocols produced DB solitons in agreement with idealized one-dimensional predictions (Kiehn et al., 2019).

A complementary variational approach identifies an internal oscillation eigenmode and a Goldstone mode. Linearization of the reduced ODE system yields

$g_{12}>\sqrt{g_{11}g_{22}}=g$5

so real internal oscillations require $g_{12}>\sqrt{g_{11}g_{22}}=g$6, meaning that the dark-component density must exceed the bright-component density for a bound internal mode to exist. The binding energy

$g_{12}>\sqrt{g_{11}g_{22}}=g$7

is proportional to the intercomponent coupling interaction, and sufficiently large phase imprint on the bright component can unbind the composite state (Alotaibi et al., 2016).

5. Stability, bifurcations, and beyond-mean-field dynamics

Linear stability theory for dark–bright structures is typically based on Bogoliubov–de Gennes linearization, where nonzero imaginary parts of eigenfrequencies signal dynamical instability. In cigar-shaped condensates, instability can arise when the anomalous mode collides with a positive-energy mode, creating a complex quartet and inducing oscillatory growth and decay of DB amplitude; for large occupation of the dark-supporting component, spontaneous transverse symmetry breaking produces internal transverse oscillatory modes and further reduces axial oscillation frequency (Middelkamp et al., 2010).

The stability landscape broadens significantly in higher dimensions. For dark–bright ring solitons in two-component Bose–Einstein condensates, the bright filling species has a stabilizing effect on the ring dark soliton. In the large-density regime, the ring radius obeys an effective radial equation of motion derived from an energy expression proportional to the one-dimensional DB energy per unit length times the circumference. Near the linear limit, symmetry-breaking bifurcations generate dark–bright soliton stripes and vortex–bright clusters, and the critical value $g_{12}>\sqrt{g_{11}g_{22}}=g$8 increases with $g_{12}>\sqrt{g_{11}g_{22}}=g$9, explaining why bright filling delays the onset of instability (Stockhofe et al., 2011).

In the unequal-dispersion setting, not only the ground-state DB soliton but also excited bright states with one or more zero crossings can be continued into the nonlinear regime. Their existence requires $$\Psi(x,t)=u(\xi),\qquad \Phi(x,t)=e^{\,i\bigl((\lambda+\tfrac{c^2}{4})t-\tfrac{c}{2}x\bigr)}\,v(\xi), \qquad \xi=x-ct,$$0, but higher $$\Psi(x,t)=u(\xi),\qquad \Phi(x,t)=e^{\,i\bigl((\lambda+\tfrac{c^2}{4})t-\tfrac{c}{2}x\bigr)}\,v(\xi), \qquad \xi=x-ct,$$1 leads to narrower stability windows and larger growth rates. Direct simulations show that unstable excited states may wobble, break up, fuse bright peaks, or relax to lower-$$\Psi(x,t)=u(\xi),\qquad \Phi(x,t)=e^{\,i\bigl((\lambda+\tfrac{c^2}{4})t-\tfrac{c}{2}x\bigr)}\,v(\xi), \qquad \xi=x-ct,$$2 states plus radiation; even the $$\Psi(x,t)=u(\xi),\qquad \Phi(x,t)=e^{\,i\bigl((\lambda+\tfrac{c^2}{4})t-\tfrac{c}{2}x\bigr)}\,v(\xi), \qquad \xi=x-ct,$$3 state may become unstable in a weak parabolic trap through a negative-Krein mode (Charalampidis et al., 2014).

Mean-field robustness is also not absolute. A beyond-mean-field treatment with ML-MCTDHB shows that fragmentation and interspecies entanglement strongly affect single-soliton oscillations and collisions. An off-center parent DB can split into a fast and a slow daughter solitary wave, a process described as being in direct contrast to the predictions of the mean-field approximation. In collisions, multiple entanglement modes can produce outer and inner DB pairs, while dark–antidark states and domain-wall–bright complexes arise spontaneously in higher orbitals (Katsimiga et al., 2016). A widespread identification of dark–bright solitons with indefinitely stable single-orbital Gross–Pitaevskii objects is therefore only an approximation valid in specific atom-number and velocity regimes.

6. Extensions across media, geometries, and component number

The dark–bright mechanism extends beyond atomic condensates. In defocusing nonlocal nematic liquid crystals, a multiscale expansion of a coupled nonlocal nonlinear Schrödinger system yields an effective Mel’nikov system with explicit one-soliton profiles: one field is bright and sech-shaped on zero background, the other is a dark dip on a continuous-wave background, and the algebraic parameter relation links their amplitudes through mutual guiding (Horikis et al., 2016).

In nonlinear isotropic chiral metamaterials, reductive perturbation theory reduces Maxwell’s equations for the two Beltrami components to a pair of coupled nonlinear Schrödinger equations. In a spectral subinterval

$$\Psi(x,t)=u(\xi),\qquad \Phi(x,t)=e^{\,i\bigl((\lambda+\tfrac{c^2}{4})t-\tfrac{c}{2}x\bigr)}\,v(\xi), \qquad \xi=x-ct,$$4

with sufficiently large rotatory strength, the system approaches the Manakov limit, and exact dark–bright vector solitons exist in which the dark notch of the positive-index mode traps a bright pulse in the negative-index mode (Tsitsas et al., 2011).

In one-dimensional saturable photorefractive waveguide arrays, coupled dark–bright gap states occur with both symbiotic and non-symbiotic character. Their existence depends on the placement of propagation constants relative to Bloch-band edges, and all four reported families exhibit weak spectral instabilities with $$\Psi(x,t)=u(\xi),\qquad \Phi(x,t)=e^{\,i\bigl((\lambda+\tfrac{c^2}{4})t-\tfrac{c}{2}x\bigr)}\,v(\xi), \qquad \xi=x-ct,$$5, corresponding to growth rates $$\Psi(x,t)=u(\xi),\qquad \Phi(x,t)=e^{\,i\bigl((\lambda+\tfrac{c^2}{4})t-\tfrac{c}{2}x\bigr)}\,v(\xi), \qquad \xi=x-ct,$$6, which nevertheless permit experimental observation over relevant propagation distances (Dong et al., 2011).

Driven resonators add a dissipative variant. In a Kerr Fabry–Pérot cavity with vectorial polarization components and normal dispersion, stationary and dynamical vectorial dark–bright solitons are formed from locked switching fronts. Their branches exhibit collapsed snaking, and they can undergo Hopf bifurcations under detuning scans. Interacting oscillating dark–bright solitons display anti-phase dynamics, then quasi-periodic oscillations, and finally in-phase dynamics as the cavity length is increased (Campbell et al., 22 Sep 2025).

Multi-component generalizations further enlarge the branch structure. In a three-component repulsive Manakov model, nondegenerate dark–bright–bright solitons possess four distinct branches, comprising two positive-mass and two negative-mass branches, and the extension to an $$\Psi(x,t)=u(\xi),\qquad \Phi(x,t)=e^{\,i\bigl((\lambda+\tfrac{c^2}{4})t-\tfrac{c}{2}x\bigr)}\,v(\xi), \qquad \xi=x-ct,$$7-component system yields $$\Psi(x,t)=u(\xi),\qquad \Phi(x,t)=e^{\,i\bigl((\lambda+\tfrac{c^2}{4})t-\tfrac{c}{2}x\bigr)}\,v(\xi), \qquad \xi=x-ct,$$8 branches grouped into $$\Psi(x,t)=u(\xi),\qquad \Phi(x,t)=e^{\,i\bigl((\lambda+\tfrac{c^2}{4})t-\tfrac{c}{2}x\bigr)}\,v(\xi), \qquad \xi=x-ct,$$9 disjoint dispersion loops (Wang et al., 7 Dec 2025). This suggests that the familiar two-component dark–bright soliton is the simplest member of a much richer hierarchy of vector solitary waves.

Taken together, these results define vectorial dark–bright solitons as a broad nonlinear-wave class rather than a single integrable solution type. Their common core is the trapping of a bright excitation by a dark background defect through intercomponent coupling; their detailed realization depends on dispersion, miscibility, dimensionality, confinement, nonlocality, lattice structure, drive and dissipation, and the many-body level of description.