Unveiling diverse solitons in the quintic perturbed Gerdjikov-Ivanov model via a modified extended mapping method.

The quintic perturbed Gerdjikov-Ivanov equation, a non-linear model in optics and quantum field theory, describes the propagation of optical pulses in nonlinear media with quintic nonlinearity and perturbation effects. This study aims to derive exact traveling wave solutions for the quintic perturbed Gerdjikov-Ivanov equation using the modified extended mapping method. The method efficiently generates a broad spectrum of solutions, including bright, dark, periodic, singular periodic, hyperbolic, plane, Weierstrass, and Jacobi elliptic forms, extending the known solution space. Compared to previous techniques, such as the generalized exponential rational function and Kudryashov's methods, the modified extended mapping method provides a more diverse set of analytical solutions with improved computational efficiency. Graphical representations using Mathematica illustrate the physical properties and stability of these solutions, confirming their relevance to optical communication and nonlinear wave phenomena. This work advances the understanding of soliton dynamics in nonlinear media and demonstrates the potential of the modified EM method in solving complex non-linear partial differential equations.