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.
