An approximate analytical solution of the Balitsky–Kovchegov (BK) equation using the homotopy perturbation method (HPM) is suggested in this work. We carried out our work in perturbative Quantum Chromodynamics (QCD) (pQCD) dipole picture of deep inelastic scattering (DIS). The BK equation in momentum space with some change of variables and truncation of the Balitsky–Fadin–Kuraev–Lipatov (BFKL) kernel can be reduced to Fisher–Kolmogorov–Petrovsky–Piscounov (FKPP) equation. The observed geometric scaling phenomena are similar to the travelling wave solution of the FKPP equation. We solved the BK equation using the HPM. The obtained solution in this work also suggests the travelling wave nature of the measured scattering amplitude [Formula: see text] plotted at various rapidities. We also extracted the saturation momentum, [Formula: see text], from the obtained solution and plotted it against different rapidities. The result obtained in this work can be helpful for various phenomenological studies in high-density QCD.