Propagation of nonlinear waves: solutions for Rossby, Bright, and Rogue waves of white dwarf in Sirius-like systems

Nonlinear waves are of great importance in understanding the behaviour and evolution of physical systems. In this study, we investigated three types of nonlinear wave phenomena—Rossby waves, bright soliton waves, and rogue waves—that occur in white dwarf (WD) plasma within Sirius-Like Systems (SLSs) in astrophysical environment. The main objective was to explore how various plasma parameters, including density and magnetic field strength, influenced the characteristics, such as amplitude and frequency, of these nonlinear waves. By gaining insights into these processes, we can enhance our understanding of similar occurrences elsewhere in the universe and deepen our knowledge of this specific environment. To achieve this goal, we employed a combination of theoretical and numerical studies to analyse how these waves behave under different conditions and solve the complex Ginzburg–Landau (cGL) equation. Specifically, we use the standard reductive perturbation method combined with quantum hydrodynamical equations and two Poisson equations to obtain the cGL equation. We then solved the cGL equation using direct and rational solution methods, which resulted in a set of analytical solutions that reflected possible propagation among various nonlinear structures. The findings of this research have significant implications for a better comprehension of nonlinear wave processes in astrophysical environments, such as SLSs. This knowledge will provide deeper insight into the physical mechanisms inside stars or celestial bodies.