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In this paper we have studied the onset of holographic $s$-wave condensate inthe $(4+1)$ dimensional planar Gauss-Bonnet-AdS black hole background withseveral non-linear corrections to the gauge field. In the probe limit,performing explicit analytic computations, with and without magnetic field, wefound that these higher order corrections indeed affect various quantitiescharacterising the holographic superconductors. Also, performing a comparativestudy of the two non-linear electrodynamics it has been shown that theexponential electrodynamics has stronger effects on the formation of the scalarhair. We observe that our results agree well with those obtained numerically[Z. Zhao et. al., Nucl. Phys. B 871 [FS] (2013) 98].

Holographic $s$-wave condensation and Meissner-like effect in Gauss-Bonnet gravity with various non-linear corrections