Ion acoustic and spin electron acoustic cnoidal waves in a spin polarized plasma with exchange effects

Separate spin evolution-quantum hydrodynamic model is employed to address the nonlinear propagation of ion acoustic wave (IAW) and spin electron acoustic wave (SEAW) in a spin polarized electron–ion plasma. The analysis has been made under the self-consistent field approximation and with exchange–correlation effects. The reductive perturbation method (RPM) is used to derive Korteweg–de Vries equation and its cnoidal wave solutions. We noted that the phase velocity of IAW in the self-consistent field approximation is almost constant however, in the presence of exchange–correlation potential there is an abrupt change in phase velocity. The phase velocity of SEAW decreases in the presence of exchange-correlation effects as compared to self-consistent field approximation. We have calculated the condition for the existence of nonlinear structures and it is found that in the presence of exchange effect the condition is satisfied for certain values of η (spin polarization factor) at different densities. Furthermore, the comparisons have been made with and without exchange effects—it shows that although the nonlinear profiles of both waves are significantly affected with exchange effect, it also converts cnoidal structures of SEAW from rarefactive to compressive. The influence of exchange–correlation potential and spin polarization on the profiles of both nonlinear structures is evaluated numerically. The present study may be helpful to understand the formation of new longitudinal cnoidal structures in laboratory degenerate plasma.