Chaotic evolution of shock, soliton, and solitary-shock waves in a degenerate quantum plasma with adiabatically trapped electrons

Nonlinear coupled drift ion acoustic waves (NCDIAWs) in partially degenerate quantum plasmas with adiabatically trapped electrons have a wide range of implications in compact astrophysical objects such as white dwarfs and neutron stars and applications in laboratory plasmas at extremely low temperatures. The nonlinear evolution equation of motion, characterized by a complex fractional 3/2 power nonlinearity is derived using the mixed kinetic and fluid model. The evolution of NCDIAWs is explored through a nonlinear planar dynamical system incorporating Burgers, Korteweg–de Vries (KdV), and KdV-Burgers equations, and the impact of an external periodic force is examined. A range of analytical and numerical tools, including phase plane theory, Sagdeev potential, linear stability analysis, Poincaré sections, fast Fourier transform, sensitivity analysis, Lyapunov exponents, and bifurcation analysis, are employed to investigate the nonlinear dynamics under plasma parameters, particularly relevant to white dwarfs. Solutions to the Burgers equation yield a pair of shock waves, while the KdV equation produces compressive solitons, and the KdV-Burgers equation generates solitary-shock waves. The introduction of external periodic forces into these dynamical systems reveals diverse behaviours, including quasiperiodic, aperiodic, and chaotic characteristics. The excitation frequency (ω) and amplitude (f0) of the external periodic force significantly influence these transitions. Frequencies far from the resonant region induce quasiperiodic behaviour, whereas frequencies near or within the resonant region exhibit a range of dynamical states, such as quasiperiodic, aperiodic, and chaotic modes. Notably, for excitation frequencies close to the system's natural frequency, the Burgers equation exhibits phenomena like quasiperiodic motion, mode-locking and unlocking, aperiodic states, as well as single-well and double-well chaos, marking an unexplored area in this domain.