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.

这项研究的主要目的是通过利用李对称方法找到理论物理中一个重要的可积模型的新的和更精确的封闭形式解，即耦合 Gerdjikov-Ivanov 方程。已实施李群分析以找到无穷小发生器和对称约简。耦合的 Gerdjikov-Ivanov 方程通过对称约简方法被简化为非线性常微分方程组。此外，已经通过收敛分析导出了简化方程组的幂级数解。通过考虑由此产生的对称性，通过调用 Ibragimov 提出的“新守恒定理”，已经提取了耦合 Gerdjikov-Ivanov 方程的守恒定律。