Abstract
A variety of soliton solutions of a common shape of the nonlinear Schrödinger equation with time-dependent coefficients is investigated via the extended tanh expansion method. This model was appealing to many researchers when its coefficients vary with time because they are closer to the naturalistic circumstances and they have a variety of soliton structures than the other classical ones (they able to model the slowly-changing inhomogeneities, external forces and non-uniformities of boundaries). A bundle of strands can be utilized to create a gadget called an endoscope or a fiberscope. Typically a long, lean test that can be put into a little gap, that will send a picture of what is interior through the fiber of a camera. Endoscopes are used by doctors to see inside the human body and are sometimes used by engineers to see inside tight spaces in machines. The four kinds of bizarre non-Kerr laws deliberated in this work are a quadratic-cubic law, an anticipates law, a cubic-quintic-septic law, and the triple-power law. Finally, 3D graphs are drawn for some acquired solutions. These solutions show that the suggested scheme is effective, reliable and simple for solving different types of nonlinear differential equations.