Approximate Closed-form Solutions for the Rabinovich System via the Optimal Auxiliary Functions Method

Based on some geometrical properties of the Rabinovich system the closed-form solutions of the equations has been established. Moreover the Rabinovich system is reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions are built using the Optimal Auxiliary Functions Method (OAFM). A good agreement between the analytical and corresponding numerical results has been performed. The accuracy of the obtained results emphasizes that this procedure could be successfully applied for more dynamical systems with these geometrical properties.