Wave patterns generated by a flow of two-component Bose-Einstein condensate with spin-orbit interaction past a localized obstacle

It is shown that spin-orbit interaction leads to drastic changes in wave patterns generated by a flow of two-component Bose-Einstein condensate (BEC) past an obstacle. The combined Rashba and Dresselhaus spin-orbit interaction affects in different ways two types of excitations---density and polarization waves---which can propagate in a two-component BEC. We show that the density and polarization "ship wave" patterns rotate in opposite directions around the axis located at the obstacle position and the angle of rotation depends on the strength of spin-orbit interaction. This rotation is accompanied by narrowing of the Mach cone. The influence of spin-orbit coupling on density solitons and polarization breathers is studied numerically.Comment: 5 pages, 3 figure

Stability of localized modes in PT-symmetric nonlinear potentials

We report on detailed investigation of the stability of localized modes in the nonlinear Schrodinger equations with a nonlinear parity-time (alias PT) symmetric potential. We are particularly focusing on the case where the spatially-dependent nonlinearity is purely imaginary. We compute the Evans function of the linear operator determining the linear stability of localized modes. Results of the Evans function analysis predict that for sufficiently small dissipation localized modes become stable when the propagation constant exceeds certain threshold value. This is the case for periodic and $\tanh$-shaped complex potentials where the modes having widths comparable with or smaller than the characteristic width of the complex potential are stable, while broad modes are unstable. In contrast, in complex potentials that change linearly with transverse coordinate all modes are stable, what suggests that the relation between width of the modes and spatial size of the complex potential define the stability in the general case. These results were confirmed using the direct propagation of the solutions for the mentioned examples.Comment: 6 pages, 4 figures; accepted to Europhysics Letters, https://www.epletters.net

Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media

We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in appearance of stability (instability) bands in focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolor periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns.Comment: 29 pages, 10 figure

Gray spatial solitons in nonlocal nonlinear media

We study gray solitons in nonlocal nonlinear media and show that they are stable and can form bound states. We reveal that gray soliton velocity depends on the nonlocality degree, and that it can be drastically reduced in highly nonlocal media. This is in contrast to the case of local media, where the maximal velocity is dictated solely by the asymptotic soliton amplitude

Dissipative surface solitons in periodic structures

We report dissipative surface solitons forming at the interface between a semi-infinite lattice and a homogeneous Kerr medium. The solitons exist due to balance between amplification in the near-surface lattice channel and two-photon absorption. The stable dissipative surface solitons exist in both focusing and defocusing media, when propagation constants of corresponding states fall into a total semi-infinite and or into one of total finite gaps of the spectrum (i.e. in a domain where propagation of linear waves is inhibited for the both media). In a general situation, the surface solitons form when amplification coefficient exceeds threshold value. When a soliton is formed in a total finite gap there exists also the upper limit for the linear gain.Comment: 5 pages, 3 figures, to appear in Europhysics Letter

Nonlinearity-induced broadening of resonances in dynamically modulated couplers

We report the observation of nonlinearity-induced broadening of resonances in dynamically modulated directional couplers. When the refractive index of the guiding channels in the coupler is harmonically modulated along the propagation direction and out-of-phase in two channels, coupling can be completely inhibited at resonant modulation frequencies. We observe that nonlinearity broadens such resonances and that localization can be achieved even in detuned systems at power levels well below those required in unmodulated couplers.Comment: 14 pages, 4 figures, to appear in Optics Letter

Nonlinear waves of polarization in two-component Bose-Einstein condensates

Waves with different symmetries exist in two-component Bose-Einstein condensates (BECs) whose dynamics is described by a system of coupled Gross-Pitaevskii (GP) equations. A first type of waves corresponds to excitations for which the motion of both components is locally in phase. In the second type of waves the two components have a counter-phase local motion. In the case of different values of inter- and intra-component interaction constants, the long wave-length behavior of these two modes corresponds to two types of sound with different velocities. In the limit of weak nonlinearity and small dispersion the first mode is described by the well-known Korteweg-de Vries (KdV) equation. We show that in the same limit the second mode can be described by the Gardner (modified KdV) equation, if the intra-component interaction constants have close enough values. This leads to a rich phenomenology of nonlinear excitations (solitons, kinks, algebraic solitons, breathers) which does not exist in the KdV description.Comment: 10 pages, 5 figure