Lie symmetry reductions, power series solutions and conservation laws of the coupled Gerdjikov–Ivanov equation using optimal system of Lie subalgebra

The main purpose of this research is to find new and more exact closed form solutions of an important integrable model in theoretical physics namely coupled Gerdjikov–Ivanov equation by utilizing the Lie symmetry approach. Lie group analysis has been implemented to find the infinitesimal generators and symmetry reductions. The coupled Gerdjikov–Ivanov equation has been reduced into a system of nonlinear ordinary differential equations by using symmetry reduction method. Furthermore, power series solutions of the reduced system of equations have been derived with convergence analysis. By considering the resulting symmetries, conservation laws of coupled Gerdjikov–Ivanov equation have been extracted by invoking “new conservation theorem” proposed by Ibragimov.