Optical soliton solutions to the generalized nonautonomous nonlinear Schrödinger equations in optical fibers via the sine-Gordon expansion method

Abstract

This article presents soliton solutions to the generalized nonautonomous nonlinear Schrödinger equations (with time-dependent coefficients) via the sine-Gordon expansion method. A bundle of fibers can be used to make a device called an endoscope or a berscope. This is a long thin probe that can be put into a small hole, which will send an image of what is inside through the fiber to a camera. Endoscopes are used by doctors to see inside the human body, and sometimes by engineers to see inside tight spaces in machines. The four kinds of bizarre non-Kerr laws deliberated in our work are a quadratic-cubic law, an anti-cubic law, a cubic–quintic–septic law and a triple-power law. In this work, we will be correct the error in the method used. This error exists since the beginning work by this method in 1996 to date.