Dynamics of kink-dark solitons in Bose-Einstein condensates with both two- and three-body interactions

Modulation instability in helicoidal spin-orbit coupled open Bose-Einstein condensates

We introduce a vector form of the cubic complex Ginzburg-Landau equation describing the dynamics of dissipative solitons in the two-component helicoidal spin-orbit coupled open Bose-Einstein condensates (BECs), where the addition of dissipative interactions is done through coupled rate equations. Furthermore, the standard linear stability analysis is used to investigate theoretically the stability of continuous-wave (cw) solutions and to obtain an expression for the modulational instability gain spectrum. Using direct simulations of the Fourier space, we numerically investigate the dynamics of the modulational instability in the presence of helicoidal spin-orbit coupling. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the threshold for amplitude perturbations.

Dynamics of kink, antikink, bright, generalized Jacobi elliptic function solutions of matter-wave condensates with time-dependent two- and three-body interactions

By using the F-expansion method associated with four auxiliary equations, i.e., the Bernoulli equation, the Riccati equation, the Lenard equation, and the hyperbolic equation, we present exact explicit solutions describing the dynamics of matter-wave condensates with time-varying two- and three-body nonlinearities. Condensates are trapped in a harmonic potential and they exchange atoms with the thermal cloud. These solutions include the generalized Jacobi elliptic function solutions, hyperbolic function solutions, and trigonometric function solutions. In addition, we have also found rational function solutions. Solutions constructed here have many free parameters that can be used to manipulate and control some important features of the condensate, such as the position, width, velocity, acceleration, and homogeneous phase. The stability of the solutions is confirmed by their long-time numerical behavior.

Dynamics of matter-wave condensates with time-dependent two- and three-body interactions trapped by a linear potential in the presence of atom gain or loss

Bose-Einstein condensates with time varying two- and three-body interatomic interactions, confined in a linear potential and exchanging atoms with the thermal cloud are investigated. Using the extended tanh-function method with an auxiliary equation, i.e., the Lenard equation, many exact solutions describing the dynamics of matter-wave condensates are derived. An important issue is the time management of the cubic and the quintic nonlinearities by tuning the rate of exchange of atoms between the condensate and the thermal background. In addition, adjusting the strength of the linear potential, the rate of exchange of atoms, and many other free parameters allow one to control many features of the condensate such as its height, width, position, velocity, acceleration, and its direction, respectively. Full numerical solutions corroborate the analytical predictions.