Based on the cubic-quintic-septic nonlinear formulation for typical physical systems with higher-order nonlinearity, we solve the one-dimensional Gross-Pitaevskii equation, and simulate the higher-order nonlinear effects of such systems under certain experimental conditions. Through F-expansion method and modulus-phase transformation, we reach the analytical solutions of the model, and the single and double soliton solutions are identified, and the septic-order nonlinearity is shown with the special nonlinear characteristics of the system.