On the exploration of dynamical optical solitons to the modify unstable nonlinear Schrödinger equation arising in optical fibers

Nonlinear Schrödinger model is one of the important fundamental nonlinear physical model to describing the fluctuations development of optical solitons and play a important role in the demonstration of dynamical fiber optics. Therefore, in nonlinear dispersive media the propagation of waves are the area of considerable interest due to its large range of possibilities to the ultrafast light pulses and data processing in communication systems. In this research, we investigated the one of the important class of nonlinear Schrödinger equation named modified unstable nonlinear Schrödinger equation (mUNLSE), which describe time periods disturbances in slightly stable and unstable medium, and also manage the instabilities of train form modulated waves. The mUNLSE is a valuable model for understanding wave behavior in fiber optics, aiding engineers in optimizing optical fiber design and predicting various conditions. We explored the collection of optical solitons and solitary wave structures to examine the dynamical properties of the governing model on the base of powerful unified approach. The explored optical solitons demonstrated in 2D, 3D, and contour plots under the aid of computing software Mathematica and may helpful for studying the waves phenomena in nonlinear optics, solitons wave theory, optical fiber, fluid dynamics, communication system, signal transmission, computer networking, sound and heat processing system. Also, the present work provide understanding into the fundamental properties of optical solitons solutions in mUNLSE, and also its experimental consequences in the physically system. On the base of this study, the proposed approach can be utilized to study the other real and complex nonlinear evolution equations.