<p>The sine-Gordon equation, a nonlinear hyperbolic partial differential equation arises in various physical contexts such as soliton theory, superconducting Josephson junctions, and nonlinear wave propagation. In this study, we develop a numerical solution technique based on the Differential Quadrature Method(DQM) using cubic B-spline basis functions to discretize the spatial derivatives. The smoothness and local support of cubic B-splines enhance the accuracy and computational efficiency of the scheme. Temporal integration is carried out using a fourth order Runge–Kutta method. The proposed approach is applied to benchmark problems involving soliton and kink solutions of the sine-Gordon equation. Numerical results are compared with exact solutions to evaluate the accuracy, convergence and stability of the method. The computed results demonstrate that the cubic B-spline DQM effectively captures the dynamic behavior of the nonlinear hyperbolic system with high accuracy, making it a reliable tool for solving a broad class of nonlinear wave equations.</p>