Stability Investigation and Soliton Wave Analysis of the High-Dispersion Cubic–Quintic Nonlinear Schrödinger Equation

Abstract

This study employs the improved modified extended tanh function method to obtain exact solutions, including dark, bright, and singular solitons, for a high-dispersion cubic-quintic nonlinear Schrödinger equation. Graphical illustration is presented to enhance the analytical interpretation of nonlinear wave dynamics under high dispersion. The study also applies linear stability analysis to assess the physical relevance of the obtained solutions. The findings are significant for understanding wave collapse, soliton formation, and rogue wave dynamics in nonlinear systems.