New impressive analytical optical soliton solutions to the Schrödinger–Poisson dynamical system against its numerical solutions

Abstract

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.