Generation of optical and matter-wave solitons in binary systems with a periodically modulated coupling

We present a systematic study of the generation of the array of optical or matter-wave kinks (dark solitons) in the ground state (GS) of binary systems. We consider quasi-one-dimensional systems described by a pair of nonlinear Schrödinger (NLSE's) or Gross-Pitaevskii equations (GPE's), which are coupled by the linear mixing, with local strength Ω, and by nonlinear interactions. We assume the self-repulsive nonlinearity in both components, and include the effects of a harmonic trapping potential, while the nonlinear interaction between the components may be both repulsive and attractive. The model may be realized in terms of periodically modulated slab waveguides in nonlinear optics and also in Bose-Einstein condensates. Depending on the sign and strengths of the linear and nonlinear couplings between the components, the ground states in such binary systems may be symmetric, antisymmetric, or asymmetric. In this work, we introduce a periodic spatial modulation of the linear coupling, making Ω an odd or even function of the coordinate (x). The sign flips of Ω(x) strongly modify the structure of the GS in the binary system, as the relative sign of its components tends to lock to the local sign of Ω. Using a systematic numerical analysis and an analytic approximation, we demonstrate that the GS of the trapped system contains one or several kinks (dark solitons) in one component, while the other component does not change its sign. The final results are presented in the form of maps showing the number of kinks in the GS as a function of the system's parameters, with the odd (even) modulation function giving rise to the odd (even) number of the kinks. The modulation of Ω(x) also produces a strong effect on the transition between states with nearly equal and strongly unequal amplitudes of the two components.