Optical solitons for quadratic law nonlinearity with five integration schemes

This paper obtains soliton solutions to nonlinear Schrödinger's equation with quadratic nonlinearity. There are five integration schemes that are applied to retrieve these soliton solutions. These are Q-function method, G' /G-expansion scheme, Riccati equation approach and finally the mapping method along with the modified mapping method. The constraint conditions, that naturally fall out of the solution structure, guarantee the existence of these solitons. As a byproduct, snoidal waves, cnoidal waves as well as singular periodic solutions emerge, which are however not important in the field of nonlinear optics.