Mathematical analysis

Riccati equation

Geometry

Ordinary differential equation

Soliton

Physics

Nonlinear system

Nonlinear Schrödinger equation

Conformable matrix

Partial differential equation

Quintic function

Pure mathematics

Mathematics

Schrödinger equation

Quadratic equation

Quartic function

Quantum mechanics

Differential equation

Polynomial

Modern Physics Letters B

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.

The novel soliton solutions for the conformable perturbed nonlinear Schrödinger equation