Innovative integration technologies for Kaup-Newell model:
sub-picosecond optical pulses in birefringent fibers
Abstract
This research deals with the Kaup-Newell model (KNM), a class of
nonlinear Schrödinger equations with important applications in plasma
physics and nonlinear optics. Soliton solutions are essential for
analyzing nonlinear wave behaviors in different physical systems, and
the KNM is also significant in this context. The model’s ability to
represent sub-picosecond pulses makes it a significant tool for the
research of nonlinear optics and plasma physics. Overall, the KNM is an
important research domain in these areas, with ongoing efforts focused
on understanding its various solutions and potential applications. A new
version of the generalized exponential rational function method (nGERFM)
and ( G ′ G 2 ) -expansion function methods are utilized to discover
diverse soliton solutions. The nGERFM facilitates the generation of
multiple solution types, including singular, shock, singular periodic,
exponential, combo trigonometric, and hyperbolic solutions in mixed
forms. Thanks to ( G ′ G 2 ) -expansion function method, we obtain
trigonometric, hyperbolic, and rational solutions. The modulation
instability (MI) of the proposed model is examined, with numerical
simulations complementing the analytical results to provide a better
understanding of the solutions’ dynamic behavior. These results offer a
foundation for future research, making the solutions effective,
manageable, and reliable for tackling complex nonlinear problems. The
methodologies used in this study are robust, influential, and
practicable for diverse nonlinear partial differential equations
(NLPDEs); to our knowledge, for this equation, these methods of
investigation have not been explored before. The accuracy of each
solution has been verified using the Maple software program.