A radial basis function partition of unity for coupled Klein–Gordon–Zakarov equations

This article introduces a numerical approach employing the local Radial Basis Function Partition of Unity (RBF-PU) method to solve the generalized two-dimensional coupled Klein–Gordon–Zakharov (KGZ) system, describing the interaction between electromagnetic waves and charged particles in plasmas. The method utilizes the matrix representation of spatial operators to transform the system into time-dependent differential equations, solved using second-order finite difference schemes. The RBF-PU method, based on scaled Lagrangian polyharmonic splines, ensures stability and robust numerical solutions. Numerical simulations validate the effectiveness of the proposed method for solving the coupled KGZ systems.