The approximate homotopy symmetry reduction for far-field model equation

The far-field model equation is investigated by the approximate homotopy symmetry method. Homotopy series solutions are constructed through summarizing the relevant general formulas for similarity reduction solutions and similarity reduction equations of differernt orders. Similarity reduction equations of different orders are linear variable coefficients ordinary differential equations, and can be solved one by one from zero-order similarity reduction equations. The auxiliary parameter in the homotopy model affects convergence of homotopy series solutions.