We propose a reconfigurable cylindrical concentrator designed using a transformation-optics approach when the core of the device contains a material with Kerr nonlinearity. We demonstrate that in the case of focusing Kerr nonlinearity of the material in the device, it functions as an axicon-like lens with a variable focus line that can be tuned by changing the incident electromagnetic field. We also numerically study the cases where the core of the device is made of a material with defocusing Kerr nonlinearity or consists of a negative index material and predict beam splitting or localized field enhancement at the boundary of the core, respectively.
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