Dynamical structure and soliton solutions galore: investigating the range of forms in the perturbed nonlinear Schrödinger dynamical equation.

In this paper, using the Hirota bilinear method, we investigate the perturbed Gerdjikov–Ivanov equation (PGIE) for lump soliton, rogue wave, periodic and kink cross rational solutions, homoclinic breathers, M-shaped and many other interactions. All these solutions have so many real life applications for example lump wave help to study the behavior of vortices and eddies in the ocean, which are used for climate modeling and fisheries management. Rogue waves are used in maritime safety, M-shaped solitons are used in optical fiber communications to transmit data over long distances without distortion, improving the efficiency and reliability of high-speed data transmission. Breathers can be used in fiber optic systems to generate ultrafast optical pulses, which have applications in telecommunications and laser technology. We also discuss the dynamical behaviour of our solutions in various dimensions. [ABSTRACT FROM AUTHOR]