New diverse enormous soliton solutions to the Gross–Pitaevskii equation, which describes the dynamics of two dark solitons in a polarization condensate under non-resonant pumping, have
been constructed for the first time by using two different schemes. The two schemes utilized are the generalized Kudryashov scheme and the (G’/G)-expansion scheme. Throughout these two suggested schemes we construct new diverse forms solutions that include dark, bright-shaped soliton solutions, combined bright-shaped, dark-shaped soliton solutions, hyperbolic function
soliton solutions, singular-shaped soliton solutions and other rational soliton solutions. The two 2D and 3D figure designs have been configured using the Mathematica program. In addition, the
Haar wavelet numerical scheme has been applied to construct the identical numerical behavior for all soliton solutions achieved by the two suggested schemes to show the existing similarity between the soliton solutions and numerical solutions.