Ponderomotive force in a magnetized degenerate plasma: role of shear stress tensor

We study electrostatic shock structures in a degenerate, relativistic, and magnetized plasma exposed to strong laser fields. By using a reductive perturbation scheme with separate longitudinal and transverse stretched coordinates, we derive a Korteweg–de Vries–Burgers (KdV–B) equation, which includes the relativistic ponderomotive force and ion shear viscosity, often neglected in earlier models, and introduces a dissipative factor that crucially modifies shock formation. The relativistic ponderomotive force alters the nonlinear, dispersive, and dissipative coefficients of the governing equation by reducing the background electron density, while magnetic fields further tune the shock amplitude and localisation. Numerical solutions confirm the emergence of steepened electrostatic shocks whose structure is governed by the competition of nonlinearity, dispersion, and viscous dissipation. Our model highlights the combined role of magnetic fields and relativistic degeneracy in shaping shock dynamics; this contrasts with earlier studies that focused on unmagnetized plasmas. The findings are important for laser–matter interactions with solid targets in the presence of applied magnetic fields and for astrophysical settings like neutron star crusts and white dwarfs, where extreme densities and relativistic degeneracy occur together.