Abstract
•Two integration algorithms handled the study of optical solitons with anti-cubic nonlinearity.•The Q-function scheme yielded dark and singular optical solitons.•Bright and singular optical solitons emerged from extended direct algebraic method.•The existence criteria for the solitons are enumerated.
This paper obtains bright, dark and singular optical soliton solutions to the nonlinear Schrödinger's equation with anti-cubic nonlinearity. The Q− function method and extended direct algebraic method are applied. In addition to optical solitons, periodic singular solutions naturally emerge as a byproduct upon application of these integration algorithms. There are constraint conditions that guarantee the existence of soliton solutions.