Abstract
•The Schrödinger-Poisson dynamical system.•Modified Mathematical Methods.•Analytical optical soliton solutions.•Integrability and modified extended direct algebraic.
The article studies the exact traveling wave solutions to the Schrödinger-Poisson system which has applications in gravity’s role of quantum state and approximate the coupling between quantum mechanics with gravitation. Diverse exact solutions in hyperbolic, trigonometric and plane wave forms are obtain using two norms of integration. For this sake modified extended direct algebraic (MEDA) and (G′/G)-expansion techniques are used. The 3D plots and their corresponding contour graphs are also depicted. The constraints conditions for the exact of solutions are also emerged during the derivation of solution.