Interaction of oblique dark solitons in two-dimensional supersonic nonlinear Schrödinger flow

We investigate the collision of two oblique dark solitons in the two-dimensional supersonic nonlinear Schrödinger flow past two impenetrable obstacles. We numerically show that this collision is very similar to the dark solitons collision in the one-dimensional case. We observe that it is practically elastic and we measure the shifts of the solitons positions after their interaction.     

Head-on collision of ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma

The head-on collision between two ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma has been investigated. By using the extended Poincaré-Lighthill-Kuo perturbation method, we obtain the KdV equation and the analytical phase shift after the head-on collision of two solitary waves in this three-component plasma. The effects of the ratio of electron temperature to positron temperature, and the ratio of the number density of positrons to that of electrons on the phase shift are studied. It is found that these parameters can significantly influence the phase shifts of the solitons. Moreover, the compressive solitary wave can propagate in this system.     

Head-on collision of ring dark solitons in Bose--Einstein condensates

The ring dark solitons and their head-on collisions in a Bose--Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincar\'e--Lighthill--Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate $r$ according to the $r^{-1/3}$ law and depend on the initial soliton amplitude and radius.     

Dark and anti-dark vector solitons of the coupled modified nonlinear Schrödinger equations from the birefringent optical fibers

Coupled modified nonlinear Schr?dinger (CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. A new type of the Lax pair and another hierarchy of the infinitely many conservation laws are derived based on the Wadati-Konno-Ichikawa system. By means of the Hirota method, soliton solutions in the normal dispersion regime are obtained. Parametric regions for the existence of dark and anti-dark vector soliton solutions are given. Asymptotic analysis shows that the collision between two solitons (two anti-dark solitons, two dark solitons, or dark and anti-dark solitons) in each polarization direction is elastic. Moreover, there is no energy transfer between two polarization components of each vector soliton, whether dark or anti-dark vector soliton. In addition, dark and anti-dark solitons can coexist on the same background seen from the collision between the dark and anti-dark solitons in one polarization direction. Our graphical analysis shows that the parameters in the CMNLS equations not only determine the regions for the existence of dark and anti-dark soliton solutions but also control the phase and direction of the propagation of the solitons. Finally, through the linear stability analysis, the modulational instability condition is given.     

Vector kink-dark complex solitons in a three-component Bose–Einstein condensate

We investigate kink-dark complex solitons(KDCSs) in a three-component Bose–Einstein condensate(BEC) with repulsive interactions and pair-transition(PT) effects. Soliton profiles critically depend on the phase differences between dark solitons excitation elements. We report a type of kink-dark soliton profile which shows a droplet-bubble-droplet with a density dip, in sharp contrast to previously studied bubble-droplets. The interaction between two KDCSs is further investigated. It demonstrates some striking particle transition behaviours during their collision processes, while soliton profiles survive after the collision. Additionally, we exhibit the state transition dynamics between a kink soliton and a dark soliton. These results suggest that PT effects can induce more abundant complex solitons dynamics in multi-component BEC.     

Interaction of solitary waves in magnetized warm dusty plasmas with dust charging effects

In consideration of adiabatic dust charge variation, the combined effect of the external magnetized field and the dust temperature on head-on collision of the three-dimensional dust acoustic solitary waves is investigated. By using the extended Poincar\'e--Lighthill--Kuo method, the phase shifts and the trajectories of two solitons after the collision are obtained. The effects of the magnitude and the obliqueness of the external magnetic field and the dust temperature on the solitary wave collisions are discussed in detail.     

Dust ion‐acoustic solitons collision in weakly relativistic plasmas with superthermality‐distributed electrons and positrons: Higher‐order phase shifts

The higher‐order (H‐O) phase shift of dust ion‐acoustic solitons (DIASs) in a weakly relativistic plasma is examined considering the influence of both superthermality‐distributed electrons and positrons. Employing the extended Poincaré–Lighthill–Kuo method (EPLKM), the Korteweg–de Vries equations (KdVEs) and the deviation in trajectories of DIASs (i.e., phase shifts) are obtained after the collision. For obtaining H‐O phase shifts of DIASs, the fifth‐order dispersion terms are added into KdVEs. The effects of the relativistic factor for a weakly relativistic regime and the superthermality of both electrons and positrons on the H‐O phase shifts are discussed. Numerical analysis gives rise to important highlights on the excitation and the collision of DIASs in astrophysical situations such as a pulsar magnetosphere.     

Collision dynamics of two Bose–Einstein condensates in the presence of Raman coupling

A collision of two-component Bose-Einstein condensates in the presence of Raman coupling is proposed and studied by numerical simulations. Raman transitions are found to be able to reduce collision-produced irregular excitations by forming a time-averaged attractive optical potential. Raman transitions also support a kind of dark soliton pair in two-component Bose-Einstein condensates. Soliton pairs and their remnant single solitons are shown to be controllable by adjusting the initial relative phase between the two colliding condensates or the two-photon detuning of Raman transitions. Received: 5 February 2001 / Published online: 27 April 2001     

Phase measurements of ring dark solitons

A four-frame technique for interferogram analysis is used to measure the transverse phase distribution of nonlinearly split 2D dark beams. Pairs of diametrical phase shifts within each ring are retrieved from the experiment. This result is one of the tests required to denote the formations observed as ring dark solitons.     

The collisions of two ion acoustic solitary waves in a magnetized nonextensive plasma

Using the extended Poincaré-Lighthill-Kuo (EPLK) method, the interaction between two ion acoustic solitary waves (IASWs) in a multicomponent magnetized plasma (including Tsallis nonextensive electrons) has been theoretically investigated. The analytical phase shifts of the two solitary waves after interaction are estimated. The proposed model leads to rarefactive solitons only. The effects of colliding angle, ratio of number densities of (positive/negative) ions species to the density of nonextensive electrons, ion-to-electron temperature ratio, mass ratio of the negative-to-positive ions and the electron nonextensive parameter on the phase shifts are investigated numerically. The present results show that these parameters have strong effects on the phase shifts and trajectories of the two IASWs after collision. Evidently, this model is helpful for interpreting the propagation and the oblique collision of IASWs in magnetized multicomponent plasma experiments and space observations.     

Painlevé Analysis,Soliton Collision and Bäcklund Transformation for the (3+1)-Dimensional Variable-Coefficient Kadomtsev-Petviashvili Equation in Fluids or Plasmas

In this paper, we investigate a (3+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili equation, which can describe the nonlinear phenomena in fluids or plasmas. Painlevé analysis is performed for us to study the integrability, and we find that the equation is not completely integrable. By virtue of the binary Bell polynomials, bilinear form and soliton solutions are obtained, and Bäcklund transformation in the binary-Bell-polynomial form and bilinear form are derived. Soliton collisions are graphically discussed: the solitons keep their original shapes unchanged after the collision except for the phase shifts. Variable coefficients are seen to affect the motion of solitons: when the variable coefficients are chosen as the constants, solitons keep their directions unchanged during the collision; with the variable coefficients as the functions of the temporal coordinate, the one soliton changes its direction.     

Two-dimensional dark soliton in the nonlinear Schrödinger equation

Two-dimensional gray solitons to the nonlinear Schrödinger equation are numerically created by two processes to show its robustness. One is transverse instability of a one-dimensional gray soliton, and another is a pair annihilation of a vortex and an antivortex. The two-dimensional dark solitons are anisotropic and propagate in a certain direction. The two-dimensional dark soliton is stable against the head-on collision. The effective mass of the two-dimensional dark soliton is evaluated from the motion in a harmonic potential.     

Controlling the collision between two solitons in the condensates by a double-barrier potential

We present an analytical solution of two solitons of Bose-Einstein condensates trapped in a double-barrier potential by using a multiple-scale method.In the linear case,we find that the stable spots of the soliton formation are at the top of the barrier potential and at the region of barrier potential absence.For weak nonlinearity,it is shown that the height of the barrier potential has an important effect on the dark soliton dynamical properties.Especially,in the case of regarding a double-barrier potential as the output source of the solitons,the collision spots between two dark solitons can be controlled by the height of the barrier potential.     

PERTURBED SPATIAL DARK SOLITONS

Effect of perturbations on spatial dark optical solitons is studied analytically with a novel direct perturbation approach for dark solitons. The problems of two-photon absorption and gain with saturation are reconsidered. The corresponding shifts of the soliton centers which have never been obtained by previous theories are given.     

Dark-bright discrete solitons: A numerical study of existence, stability and dynamics

In the present work, we numerically explore the existence and stability properties of different types of configurations of dark-bright solitons, dark-bright soliton pairs and pairs of dark-bright and dark solitons in discrete settings, starting from the anti-continuum limit. We find that while single discrete dark-bright solitons have similar stability properties to discrete dark solitons, their pairs may only be stable if the bright components are in phase and are always unstable if the bright components are out of phase. Pairs of dark-bright solitons with dark ones have similar stability properties as individual dark or dark-bright ones. Lastly, we consider collisions between dark-bright solitons and between a dark-bright one and a dark one. Especially in the latter and in the regime where the underlying lattice structure matters, we find a wide range of potential dynamical outcomes depending on the initial soliton speed.     

Gray and dark spatial solitons supported by two-photon isomerization

A theory is presented to show that gray and dark solitons can exist in bulk polymers with two-photon isomerization (TPI) nonlinearity. The soliton FWHM, intensity and phase profiles are discussed in detail. In addition, the stability properties of these TPI solitons are also investigated by employing the stability criterion based on the renormalized momentum.     

Soliton dynamical properties of Boseben Einstein condensates trapped in a double square well potential

We first present an analytical solution of the single and double solitions of Bose-Einstein condensates trapped in a double square well potential using the multiple-scale method. Then, we show by numerical calculation that a dark soliton can be transmitted through the square well potential. With increasing depth of the square well potential, the amplitude of the dark soliton becomes larger, and the soliton propagates faster. In particular, we treat the collision behaviour of the condensates trapped in either equal or different depths of the double square well potential. If we regard the double square well potential as the output source of the solitons, the collision locations (position and time) between two dark solitons can be controlled by its depth.     

Temporal behavior of dark spatial solitons in closed-circuit photovoltaic media

We show that the time-dependent nonlinear wave equation in closed-circuit photovoltaic media can exhibit quasi-steady-state and steady-state spatial solitons. We demonstrate that the formation time of open-circuit quasi-steady-state and open-circuit steady-state dark solitons decreases with an increase in the intensity ratio of the soliton, which is the ratio between the soliton peak intensity and the dark irradiance. We find that for the time-dependent nonlinear wave equation that exhibits only an open-circuit steady-state dark soliton, changing the electric current density J₀ does not generate quasi-steady-state dark solitons and affects the formation time of steady-state dark solitons and that for the time-dependent nonlinear wave equation that exhibits an open-circuit quasi-steady-state dark soliton, changing J₀ gives rise to three different time evolution regimes of the full width half maximum of the soliton’s intensity. The first regime shows that the formation time of steady-state dark solitons increases with J₀ whereas the formation time of quasi-steady-state dark solitons is independent of J₀. The second regime shows that the formation time of steady-state dark solitons decreases with an increases in J₀ and the formation time of quasi-steady-state dark solitons increases with J₀. The third regime shows that changing J₀ enables only steady-state dark solitons in the time-dependent nonlinear wave equation, of which the formation time increases with J₀.     

Control of interaction between femtosecond dark solitons in inhomogeneous optical fibers

In this paper, we present exact femtosecond one- and two-dark soliton solutions for a variable-coefficient higher-order nonlinear Schrödinger equation via modified Hirota method. The propagation and interaction of femtosecond dark solitons are investigated in inhomogeneous fiber systems. Elastic collision, bound oscillation and parallel propagation can be achieved in both Gaussian distributed parameter system and exponentially periodic distributed parameter system by choosing the appropriate distributed parameters and soliton parameters. The results may be beneficial to the realization of interaction control of femtosecond dark solitons in communication systems.