This paper presents an equation for the small-x evolution of the $ F_2 $ structure function of a large nucleus, incorporating multiple pomeron exchanges in the leading logarithmic approximation using Mueller's dipole model. The evolution equation is derived from the dipole wave function, which includes all multiple pomeron exchanges. In the double leading logarithmic limit, this equation reduces to the GLR equation. The paper discusses the importance of multiple pomeron exchanges in describing experimental data, such as ZEUS 1995 data, which may indicate saturation of the $ F_2 $ structure function at low $ Q^2 $. The authors derive an equation for the evolution of the $ F_2 $ structure function of a nucleus in the leading logarithmic approximation, which is a non-linear integral equation, not a functional differential equation. The equation is shown to reduce to the GLR equation in the double logarithmic limit. The paper also discusses the limitations of the large $ N_c $ approximation and the advantages of the approach used. The results are compared with previous works, and the paper concludes that the dipole model provides a straightforward way to include multiple pomeron exchanges in the evolution equation. The paper also notes that the inclusion of pomeron fusion effects in the dipole wave function is a difficult task and remains an open problem. The authors also mention that the results could be used to fit recent HERA data.This paper presents an equation for the small-x evolution of the $ F_2 $ structure function of a large nucleus, incorporating multiple pomeron exchanges in the leading logarithmic approximation using Mueller's dipole model. The evolution equation is derived from the dipole wave function, which includes all multiple pomeron exchanges. In the double leading logarithmic limit, this equation reduces to the GLR equation. The paper discusses the importance of multiple pomeron exchanges in describing experimental data, such as ZEUS 1995 data, which may indicate saturation of the $ F_2 $ structure function at low $ Q^2 $. The authors derive an equation for the evolution of the $ F_2 $ structure function of a nucleus in the leading logarithmic approximation, which is a non-linear integral equation, not a functional differential equation. The equation is shown to reduce to the GLR equation in the double logarithmic limit. The paper also discusses the limitations of the large $ N_c $ approximation and the advantages of the approach used. The results are compared with previous works, and the paper concludes that the dipole model provides a straightforward way to include multiple pomeron exchanges in the evolution equation. The paper also notes that the inclusion of pomeron fusion effects in the dipole wave function is a difficult task and remains an open problem. The authors also mention that the results could be used to fit recent HERA data.