Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method

Abstract

We give a more generalized treatment of the 1D generalized Gross-Pitaevskii equation (GGPE) with variable term coefficients. External harmonic trapping potential is fully considered and the nonlinear interaction term is of arbitrary polytropic index of superfluid wave function. We also eliminate the interdependence between variable coefficients of the equation terms avoiding the restrictions that occur in some other works. The exact soliton solutions of the GGPE are obtained through the delicate combined utilization of modified lens-type transformation and F-expansion method with dominant features like soliton type properties highlighted.

Sonic horizon dynamics of ultracold Fermi system under elongated harmonic potential

“…This is done by solving the onedimensional time-dependent GPE for the system in an elongated harmonic trap. The one-dimensional GPE used here can be expressed as [23] i…”

“…We use a variational method to obtain a quantitative description of the dynamical evolution of the system. According to the analytical results from prior work, [23][24][25] the bright soliton solution can be obtained from Eq. ( 1), so the ansatz for the wave function ψ(x/σ (t),t) is set to sech 1/γ (x/σ (t),t).…”

Bright Soliton Solution of (1+1)-Dimensional Quantum System with Power-Law Dependent Nonlinearity

“…It is a very effective method to solve partial differential equations such as NLSE. Basically, it is implemented by expressing the solutions of the equations in the form of power expansion of Jacobian function [18,19]. Moreover, for the nonlinear study of the NLSE, the soliton-type solution is usually the ultimate goal of the analytical solution search.…”