On the bright and singular optical solitons to the ($2+1$)-dimensional NLS and the Hirota equations

This study constructs bright and singular optical solitons the ($2+1$)-dimensional NLSE and the Hirota equation by utilizing the new sine-Gordon expansion method. The parametric conditions for the existence of valid solitons are given. We give the variations of solitary and periodic wave solutions that depend on the parameters. We present the 2D, 3D and contour graphs to represent the kind of solutions secured in this study.