A Conservative Finite Difference Scheme of Second‐Order Accuracy for the Solution of Davey–Stewartson Equations

ABSTRACT This work investigates a nonlinear conservative finite difference scheme of second‐order accuracy for the Davey–Stewartson (DS) equations, a model of nonlinear dispersive wave equations. The proposed numerical scheme is shown to satisfy key properties including conservativeness, uniqueness of solutions, and stability. The existence of approximate solutions and convergence of the difference scheme are established, with the convergence rate proven to be under the uniform norm without restrictions on mesh sizes. As an application, fundamental line rogue waves of DS equations are studied numerically in detail, depicting emergence from and decay back to a constant background. Finally, several numerical experiments are reviewed to validate the theoretical results and compare performance against existing methods.