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This study shows the dynamics of relativistic electrons in terms of Diracequation solutions when an ultra-intense short laser pulse of intensity $\ge10^{23} {W.cm^{-2}}$ propagates through magnetized dense plasma ($B_0\approx{1MG})$. The interaction dynamics is analyzed near the strong-field quantumelectrodynamics (SF-QED) regime. Our study finds new solutions in plasma mediaconsidering the effects of the re-normalized mass of relativistic electrons andthe nonzero effective mass of accelerated photons. We have provided a generalmethod for constructing exact solutions of the Dirac relativistic equation thatcorrectly explains the dynamics of electrons in the strongly magnetized plasmamedium. The modified solutions of the Dirac equation for one electron arederived and compared to the Volkov solutions. The new solutions are a basis fora feasible explanation of quantum attributes of relativistic electrons in astrong electromagnetic field of very short ultra-intense laser pulses withintensity near Schwinger field intensity. The solutions are called new Volkovsolutions in a plasma medium. These solutions can be used to understand betterthe theory of quantum radiation reaction for the next-generation laser-plasmaaccelerator. Our results show that the Volkov solutions are not applicable in amagnetized plasma medium

Volkov solutions for relativistic magnetized plasma in strong field quantum electrodynamics regime