Abstract
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.
Highlights
Black hole-related problems are fascinating subjects in fundamental physical phenomena study
Experiments demonstrated the formation of the sonic black hole together with the associated Hawking radiation in elongated Bose-Einstein condensates (BEC).2,3
For a typical quantum system such as BEC where sonic black hole is to be formed, we first investigate onedimensional nonlinear Schrödinger equation (NLSE) modeling the evolution of the system incorporating full cubic-quintic-septic nonlinearity and harmonic trapping potential
Summary
Black hole-related problems are fascinating subjects in fundamental physical phenomena study. For a typical quantum system such as BEC where sonic black hole is to be formed, we first investigate onedimensional NLSE modeling the evolution of the system incorporating full cubic-quintic-septic nonlinearity and harmonic trapping potential. For the actual study of the three-dimensional BEC where sonic black hole can be studied more generally, based on the self-similar approach, we derive the soliton-related evolution for the three-dimensional NLSE with cubic-quintic-septic nonlinearity where sonic horizon can form in a more general manner. To validate our theoretical work, we calculate the sonic horizon dynamics by deriving the system flow velocity based on the analytical soliton solution obtained for the system incorporating full cubicquintic-septic nonlinearity. The two sections demonstrate the theoretical NLSE model that incorporates cubicquintic-septic nonlinearity and the methodology for deriving the sonic horizon-related analytical solutions of the NLSE for the one-dimensional and three-dimensional cases. We derive the typical nonlinear solution of Eq (1) for three categorical orders of nonlinear interaction. we will identify the typical feature for the sonic horizon formation with septic order nonlinearity
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