Abstract:
The current study examines the stability of both bright and dark solitary wave solutions for the
Generalized Higher Order Nonlinear Schr¨odinger Equation and its Stability. The propagation of
ultrashort pulses in nonlinear mediums is described mathematically by the generalized high-order
nonlinear Schr¨odinger equation (GHNLSE). Within optical fibers, ultra-short pluse propagation is
described by the higher order nonlinear Schr¨odinger (NLS) equation. We get the accurate brilliant,
dark, and bright-dark solitary wave soliton solutions of the generalized higher order nonlinear NLS
problem by applying the amplitude ansatz approach. These exact answers to the generalized higher
order nonlinear NLS problem show the effectiveness of the approach. The modulation instability
analysis and stability analysis solutions are applied to examine the stability of these solutions
as well as the movement role of the waves. Every answer is precise and reliable.Several intriguing
characteristics of dark and bright solitons include their stability and multimodal interaction
capabilities. Their characteristics render them potentially advantageous for several applications,
including medical imaging and optical communications
