In our current study, we will derive new diverse enormous impressive analytical optical
soliton solutions for the Schrödinger–Poisson dynamical system. The proposed model
is applied in gravity field with the corresponding quantum state that produces coupling
between different gravity states. Moreover, this model has a significant role in the field of
many quantum phenomena. Hereby, we will construct diverse forms of the soliton behaviors
that arising from this dynamical system via the solitary wave ansatze method. This
technique is one of the ansatze methods that doesn’t surrenders to the homogeneous balance
and continuously achieves good results. Moreover, we will construct the numerical
solutions that are identical for all achieved exact solutions by using two-dimensional differential
transform method (TDDTM). The extracted soliton solutions are new compared with
that realized before by other authors who used various techniques. The achieved solutions
will give new distinct configurations to soliton behaviors arising from this model and show
the fact of charges regular distributions on conductors’ materials surface