Rational function solutions of higher-order dispersive cubic-quintic nonlinear Schrödinger dynamical model and its applications in fiber optics

Abstract

The study explores a series of cubic-quintic nonlinear Schrödinger equation with higher-order dispersive characteristics. This equation is also a fundamental equation in nonlinear physics that is used to depict the dynamics of femtosecond light pulses propagating through a medium with a nonlinearity profile characterized by a parabolic function. Symbolic computation is utilized, and the double $(G^{\prime }/G,1/G)$-expansion technique is applied to investigate the mathematical characteristics of this equation. Novel solitons and rational function solutions in various forms of the high-order dispersive cubic-quintic nonlinear Schrödinger equation are derived. These solutions have applications in engineering, nonlinear physics and fiber optics, providing insights into the physical nature of wave propagation in dispersive optics media. The results obtained form a basis for understanding complex physical phenomena in the described dynamical model. The computational approach employed is demonstrated to be straightforward, versatile, potent, and effective. Additionally, the presented solutions showcase various intriguing patterns, including kink-type periodic waves, combined bright-dark periodic waves, multipeak solitons, and breather-type waves. This diverse set of solutions contributes to the interpretation of the dynamical model, illustrating its complexity. Moreover, the simplicity and effectiveness of our computational technique make it applicable to solving similar models in physics and other fields of applied science.