Analytical control of multidark soliton collisions and dynamics with tunable properties

In this paper, we present an analytical description of the dynamics of dark solitons and collisions between such waves induced by the nonlinear Schrödinger equation. Using the Hirota bilinear direct method, we give intrinsic properties of these solitary waves such as velocity and depth, which can be independently tuned through spectral parameters. These same parameters allow us to describe the nonlinear interactions between N dark solitons, which manifest as phase shift transitions and give the exact trajectories of each soliton. Exact expressions for the velocity, depth, and phase shift transitions prior and upon interactions are given. Our findings offer a tunable approach to modeling dark soliton trains and their interactions in nonlinear media. The paper's approach provides valuable insight for applications in nonlinear optics, Bose–Einstein condensates, and soliton-based waveguiding platforms, where precise control of solitary wave dynamics is essential. It also confirms experimental work of dark soliton collisions in Bose–Einstein condensates.