Sonic horizon dynamics for quantum systems with cubic-quintic-septic nonlinearity

We study the sonic horizon formation problem for quantum system incorporating septic nonlinearity, which is modeled by the nonlinear Schrödinger equation (NLSE) with nonlinearity up to septic order. Based on the F-expansion method combined with modulus-phase transformation, we derived the soliton solutions of such NLSE for the one-dimensional and three-dimensional scenarios, from which the sonic horizon formation dynamical variables are derived. We identify that the distribution of system flow velocity and sound velocity, which determine the occurrence of the sonic horizon, agree well with the corresponding quantities obtained from pure numerical evaluation, demonstrating the applicability of the theoretical approach adopted in this study.