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.
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