Low frequency nonlinear electrostatic structures and chaos in relativistic degenerate inhomogeneous collisional EPI plasma with strong magnetization

Relativistic degenerate electron–positron–ion plasmas which are Landau quantized represent a fundamental state of matter in compact astrophysical objects, where extreme densities and magnetic fields govern nonlinear wave dynamics. Understanding their behavior is essential for connecting microscopic plasma processes to macroscopic phenomena. We investigate the formation and evolution of damped solitons in such plasmas by deriving a drift-damped Zakharov–Kuznetsov equation that incorporates adiabatic trapping, collisional damping, and density inhomogeneity. Analytical solitary-wave solutions show that ion–neutral collisions progressively reduce amplitude, broaden width, and slow propagation, while magnetic confinement enhances soliton amplitude until saturation due to dispersive broadening. Numerical simulations and phase-space analysis reveal transitions from damping to quasiperiodicity and chaos, confirmed by Poincaré maps, FFT spectra, and Lyapunov exponents. Variations in nonlinearity, dispersion, collisionality, and positron fraction reshape the temporal evolution, delaying or accelerating instability depending on parameter strength. Comparison of relativistic and ultrarelativistic regimes further demonstrates that while relativistic plasmas exhibit moderate damping and gradual growth, ultrarelativistic plasmas undergo stronger initial damping but faster recovery and instability due to extreme degeneracy and enhanced Landau quantization. These results establish a comprehensive framework for nonlinear dynamics in relativistic degenerate plasmas, with direct implications for astrophysical systems and experimental validation in strongly magnetized laboratory plasmas.