Is singularity-free cloaking possible? New cloaking ideas (a reply to comments on the paper “Invisible cloaking of material bodies using the wave flow method” [Phys. Usp. 53 455 (2010)])

Replies are made to comments in N N Rozanov's letter to the editors “Can even monochromatic radiation ensure ideal invisibility?” (see Usp. Fiz. Nauk 181 787 (2011) [Phys. Usp. 54 763 (2011)]) concerning our paper “Invisible cloaking of material bodies using the wave flow method” (Usp. Fiz. Nauk 180 475 (2010) [Phys. Usp. 53 455 (2010)]). Examples are given of spatial configurations that enable the creation of singularity-free cloaking materials. Some emerging cloaking ideas are discussed.