Numerical simulation of KdV equation

Abstract

It is by now well known that the 2d-non-linear KdV differential equation u + u + uu = 0 is one of the most popular and famous equations of mathematical physics. The major content of the recent work deals with the establishing of a numerical schemes, based on the finite difference, to descretize this famous equation. The latter, in it self, is not the principal focus of our work. It's exact solvability (the existence of an explicit analytic solution) is behind our motivation to develop a numerical strong approach to be tested first on this famous equation before used it for other models. The principal result of the this work is the presentation of a proof for the unconditional stability of our schemes. Other important properties are presented.