Novel Study of NLSEs with the Assistance of Different Methods

Abstract

It is noteworthy that the significance of nonlinear wave profile in nonlinear sciences and information technology has been increased rapidly for last two decades. For this purpose, many researchers studied nonlinear Schr¨odinger equations (NLSE) and vari- ous types of nonlinear evolution equations (NLEEs) appear in nonlinear optics, system of fiber communications, plasma physics, fluid dynamics, quantum physics, high en- ergy physics, acoustic gravity waves and optical fibers etc [1]. Many integrable NLEEs possess the soliton solutions which retains the speed as well as the shape, even after col- lision with each other. Several efficient techniques have been introduced in literature for obtaining soliton solutions of NLSEs and NLEEs for last two decades, e.g F-expansion approach and its modification, HBM, Lie symmetry technique, first integral method, in- verse scattering scheme, Sine-Gordon architectonic, and other approaches. In this thesis firstly, we will examine the optical solitons, the Schr¨odinger-Hirota equa- tion in the presence of chromatic dispersion. For this intent, by obtaining the multiple soliton types using the Hirota Bilinear Method (HBM), the Sine-Gordan method (SGE) and the Kudryashov method, opticall soliton solutions were obtained. We obtain some parabolic, anti-parabolic, M-shaped, W -shaped, butterflies, bright, anti-dark, V -shaped, S-shaped, and other solutions for our model. This detailed exploration provides per- ception into the dynamic behavior and interactions of nonlinear solutions in NLSHE systems. The nonlinear Schr¨odinger equation with quintic non-Kerr nonlinear term (NLSE-QNKNT) will be studied. This equation describes the nonlinear wave state of optical solitons, which is a noteworthy and important model in optical fiber communication. By using the HBM, SGE and the GK approach, the various optical solutions of the nonlinear Schr¨odinger wquation are obtained. Finally, the graphs of some obtained solutions are drawn by setting values to tha parameters. We will obtain butterfly, S and W -shaped, parabolic, dark, kink and other solitary wave solutions (SWS) for our governing model.