Approximate homotopy symmetry method: Homotopy series solutions to the sixth-order Boussinesq equation

摘要: An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the sixth-order Boussinesq equation, which arises from fluid dynamics. We summarize general formulas similarity reduction solutions equations of different orders, educing related series solutions. Zero-order are equivalent Painleve IV type equation or Weierstrass elliptic equation. Higher order can be obtained by solving linear variable coefficients ordinary differential equations. The auxiliary parameter has an effect on convergence Series retrieved method.