Investigations of dark, bright, combined dark-bright optical and other soliton solutions in the complex cubic nonlinear Schrödinger equation with δ-potential

In this study, using the extended sinh-Gordon equation expansion method, we construct the dark, bright, combined dark-bright optical, singular, combined singular solitons and singular periodic waves solutions to the complex cubic nonlinear Schrödinger equation with δ-potential. The conditions for the existence of the obtained solutions are given. To present the physical feature of the acquired result, the 2D and 3D graphs are plotted under the choice of suitable values of the parameters.