This paper presents an investigation of the self-focusing of coshGaussian laser beams in warm quantum plasma while taking into account the effects of relativistic nonlinearity. The non-linear differential equation governing the beam width parameter under the weakly relativistic nonlinearity in this study was derived from the cylindrical coordinate system. The equation has been solved numerically by using the fourth-order Runge–Kutta method. Numerical analysis has shown that the present model’s parameters, such as the decentered parameter, laser intensity, electron density of plasma, and Fermi temperature of electrons, play a vital role in propagation characteristics. Furthermore, comparisons were made for the coshGaussian laser self-focusing in warm quantum plasma, cold quantum plasma, and classical relativistic plasma. It has also been found that the cosh-Gaussian laser beam has caused better focusing in the warm quantum plasma in comparison with the Gaussian laser beam; a fact that is very important for some applications in high-power laser-dense plasma interactions.
