In this paper we introduce the confinement into the kernel of the BFKL equation, assuming that the sizes of produced dipoles cannot be large. The goal of this paper is to find how this assumption, which leads to a correct exponential decrease of the amplitude at large impact parameters, affects the main properties of the BFKL Pomeron. We solve the equations for total cross section and |b 2 | numerically and developed some methods of analytical solutions. The main result is that the modified BFKL Pomeron has the same intercept and α ′ IP = 0 as the BFKL Pomeron. It gives us a hope that the unknown confinement will change only slightly the equations of the CGC/saturation approach.Keywords: BFKL Pomeron, solutions to the BFKL equation, semi-classical approach, diffusion approximation, large impact parameter behaviour of the amplitude .

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