New classifications of nonlinear Schrödinger model with group velocity dispersion via new extended method

•To investigate the nonlinear Schrödinger equation with group velocity dispersion and second order spatiotemporal dispersion coefficients.•To reduce the governing model into classical nonlinear ordinary differential equation.•To implement new extended direct algebraic method to construct many novel mixed dark, bright and complex optical solutions.•To extract some important analytical solutions such as travelling mixed dark, bright and complex travelling wave solutions for the model.•Applications of new extended direct algebraic method in various fields of physical sciences and engineering. This work investigates the nonlinear Schrödinger equation (NLSE) with group velocity dispersion and second order spatiotemporal dispersion coefficients. The governing model is reduced into the classical nonlinear ordinary differential equation. Extended direct algebraic method (EDAM) is implemented to construct many novel mixed dark, and complex optical solutions. As a result, some important analytical solutions such as travelling mixed dark, and complex travelling wave solutions for the model are extracted.