Lie Symmetry Analysis of Fractional Kersten–Krasil’shchik Coupled KdV–mKdV System

This paper investigates the invariance properties of the fractional Kersten–Krasil’shchik coupled KdV–mKdV system. By extending Lie symmetry analysis method to a fractional system, two vector fields are derived. The similarity transformation elegantly reduces the fractional system to a set of ordinary differential equations. Furthermore, the explicit power series solutions for the system are derived by employing the power series theory. Lastly, conservation laws for the system are established utilizing Ibragimov’s method.