The Tantawy technique for modeling low-frequency ion-acoustic cnoidal waves in a magnetized degenerate astrophysical quantum plasma

This study investigates the propagation of both fractional and non-fractional ion-acoustic cnoidal waves (IACWs) in a magnetized degenerate Thomas-Fermi electron-positron-ion ( e − p − i ) plasma, incorporating the effects of magnetic fields on wave dynamics. Using the reductive perturbation method (RPM), the planar integer Korteweg-de Vries (KdV) equation is derived, accounting for the influence of the magnetic field on nonlinear wave structures. The analysis reveals the existence of positive potential (compressive) cnoidal waves, which, in the limiting case, reduce to solitary waves. The characteristics of these waves, which demonstrate how the electron-to-positron Fermi temperature ratio, positron concentration, and obliqueness affect their profile. The study’s findings are relevant to astrophysical environments and dense plasmas generated in laser-produced plasmas. For the second objective of this investigation, the integer planar KdV equation is converted to the planar fractional KdV equation (FKdV) using a suitable transformation to study the impact of the fractional order parameter on the fractional IACW profile. To this end, the planar FKdV equation is solved using the Tantawy technique and the Laplace residual power series method (LRPSM). Some approximate analytical solutions to the planar FKdV equation are derived using the two proposed approaches. The generated approximations are numerically examined and compared with the exact solution for the integer case to assess the accuracy of the derived approximations. Numerical results are constructed based on parameters relevant to dense astrophysical environments, such as white dwarfs, highlighting the significant role of the magnetic field in modifying wave behavior.