The novel soliton solutions for the conformable perturbed nonlinear Schrödinger equation

The sub-equation method is implemented to construct exact solutions for the conformable perturbed nonlinear Schrödinger equation. In this paper, we consider three different types of nonlinear perturbations: The quadratic–cubic law, the quadratic–quartic–quintic law, and the cubic–quintic–septic law. The properties of the conformable derivative are discussed and applied with the help of a suitable wave transform that converts the governing model to a nonlinear ordinary differential equation. Furthermore, the order of the expected polynomial-type solution is obtained using the homogeneous balancing approach. Dark and singular soliton solutions are derived.