Analytical traveling-wave solutions to a generalized Gross-Pitaevskii equation with some new time and space varying nonlinearity coefficients and external fields

We present analytical matter-wave solutions to a generalized Gross-Pitaevskii (GGP) equation with several new time and space varying nonlinearity coefficients and external fields. This is realized by taking a suitable similarity transformation to the GGP equation which makes the original partial differential equation into a stationary and ordinary differential equation. We report a few families of analytical solutions of the GGP equation with several new time and space varying nonlinearity interactions, in which some physically relevant soliton solutions are found. The profile features of the evolution wave functions depend on the different choices of the composite functions ξ.