Optical and singular solitary waves to the PNLSE with third order dispersion in Kerr media via two integration approaches

In this paper, the sine-Gordon expansion method (SGEM) and the generalized tanh (GTM) methods are employed to find the optical solitary wave solutions to the perturbed nonlinear Schrödinger equation (PNLSE) with Kerr law nonlinearity describing the propagation of optical solitary waves in nonlinear optical fibers. The dark, bright, dark-bright and dark-singular optical solitary waves are retrieved. Additionally, singular solitary waves are also derived as by-products of the integration scheme. Physical interpretations of the obtained results are demonstrated with interesting figures. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the PNLSE.