Dynamic generation of matter solitons from linear states via time-dependent scattering lengths

In this paper, we examine the possibility of generating bright and dark solitons, as well as multi-pulse solitary waves in Bose–Einstein condensates. Starting from the linear limit of the problem, where such solutions are known explicitly, we use 'dynamic continuation' through the temporal variation of the scattering length, which can be realized in experiments upon using external time-dependent magnetic fields. We examine the stability of the resulting solutions both through direct numerical simulations and through numerical continuation of the relevant steady states and linear stability analysis. Analytical results, illustrating the nature of the bifurcation of the nonlinear solutions, are found to be in good agreement with the numerical findings.