Multiplicity distributions in DIS for heavy nucleus

We found solutions to the linear but with complicated kernel and non-homogeneous evolution equations for the cross sections of productions of $n$-cut Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomerons in the final states of high energy DIS on a nucleus, resumming all multiple rescatterings in the leading logarithmic approximation. For the model leading-twist BFKL kernel, we calculate analytical solutions of these equations by developing the homotopy approach. We also calculate the solution in the large $z=\ln\left(x_{01}^2\,Q_s^2(Y,\mathbf{b})\right)$ and large $n\gtrsim\langle n(z) \rangle$ limits, where $x_{01}$ is the dipole size, $Q_s$ the saturation scale and $\langle n(z) \rangle$ is the average multiplicity of the produced gluons. Having these cross sections we calculate the multiplicity distributions of the produced gluons and describe how the upcoming Electron-Ion Collider (EIC) can test our theoretical formalism.