Diverse optical solitons to the nonlinear Schrödinger equation via two novel techniques

In this article, we aim to investigate the nonlinear Schrödinger equation that describes the pulse propagation in optical fiber through two novel techniques, namely, the Bäcklund transformation-based method and Wang’s direct mapping method for the first time. Diverse soliton solutions expressed in the form of trigonometric function such as sine, cosine, secant, cosecant, hyperbolic function like hyperbolic tangent, hyperbolic secant, hyperbolic cosecant, hyperbolic sine, hyperbolic cosine, exponential function and the rational function are obtained. The performances of the different soliton solutions are illustrated through the 3-D plots, 2-D contours and 2-D curves. It is confirmed that the proposed methods are powerful and effective, which can be used to study the other PDEs arising in optics.