Dynamics on novel wave structures of non-linear Schrödinger equation via extended hyperbolic function method

In this study, our focus is on the construction of novel soliton solutions of non-linear Schrödinger equation with parabolic law and non-local law non-linearities via new extended hyperbolic function method. The acquired solutions are original and could be helpful in the field of nonlinear optics, fluid dynamics, and plasma physics. From these outcomes, it is believed that this method is a promising technique to handle a wide variety of such type of equations. For physical understanding and better realization of our constructed solutions, some of the obtained solutions under appropriate parameters are demonstrated by 2D and 3D plots. Analysis discloses that the proposed scheme is consistent and can be applied to more advanced models in engineering and physics.