Computational investigation on a nonlinear dispersion model with the weak non-local nonlinearity in quantum mechanics

•Analytical handling of the nonlinear dispersion model with weak non-local nonlinearity.•Constructing novel solitary wave solutions.•Investigating the obtained results accuracy.•Explaining the obtained solutions through some distinct types of sketches. In the presence of nonlinear dispersion, we examine certain solitary wave solutions of a dimensionless nonlinear Schrödinger (DLNLS) equation with the parabolic law of nonlinearity. We use a unique computational (generalized rational (GRat)) approach to build a variety of solutions with varying shapes. These answers show how the nonlinear interaction between Langmuir waves and electrons causes the parabolic law nonlinearity. For a better visual description of the examined model, these interactions are shown using several graphs in three-, two-dimensional, and polar plots. These representations of the obtained solutions are considered as numerical simulaions to explain the investigated model’s characterizations, the pulse waves’ behaviour and the interaction between complex short wave and real long wave envelope.