Dynamics of kink, antikink, bright, generalized Jacobi elliptic function solutions of matter-wave condensates with time-dependent 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.

Solitary waves dynamic for Davydov α-helical protein model: Effects of localized and periodic inhomogeneities

We describe the dynamic of excitons through single inhomogeneous α-helical proteins with off-diagonal and diagonal couplings. Inhomogeneities considered are either localized or periodic. Intensive numerical simulations carried show stable structures and allow us to single out important features of excitons dynamic. In the absence of inhomogeneities, the interplay between off-diagonal and diagonal couplings leads to two distinct types of solitary waves. Bright solitary waves correspond to an off-diagonal coupling constant lower than a critical diagonal coupling constant, while dark solitary waves are obtained in the opposite case. Inclusion of inhomogeneities profoundly affects the profiles, amplitudes, and energies transported by the waves. For relatively small strength of inhomogeneities, only the profiles of the waves significantly change, the other properties remaining almost unchanged. Large strength inhomogeneities sensitively twist the profiles and increase amplitudes and energies of the waves. Our study suggests that small strength inhomogeneities allow a coherent transport of energy and the biological functions remain unchanged, but large strengths of inhomogeneities affect the biological functioning of the α-helical protein chains. Hence, large strengths of inhomogeneities may amplify the energy of the molecule and could be used to treat some diseases.

Exotic complexes in one-dimensional Bose-Einstein condensates with spin-orbit coupling

By means of the F-expansion method and intensive numerical simulations, the existence of three families of nonlinear matter waves including Jacobi elliptic functions, solitons, and triangular periodic functions, is demonstrated for spin-orbit coupled Bose-Einstein condensates with a linear potential. In addition, several complexes are obtained by taking two distinct solutions of each family or two distinct families. These solutions sustain different types of two-body interactions in the condensate that can be repulsive, attractive, or attractive and repulsive. Whereas the spin-orbit coupling destabilized these nonlinear matter waves, the linear potential leads to a stabilization. The numerical results are in excellent agreement with our analytical findings and it can be expected that the proposed robust solutions should be observable for experimentally relevant conditions.