In this article we study the large-time behavior of the solution to a general Rosenau type approximation to the heat equation [16], by showing that the solution to this approximation approaches the fundamental solution of the heat equation at a sub-optimal rate. The result is valid in particular for the central differences scheme approximation of the heat equation, a property which to our knowl...

Solitons and Other Solutions to Perturbed Rosenau KdV RLW Equation with Power Law Nonlinearity P. Sanchez, G. Ebadi, A. Mojaver, M. Mirzazadeh, M. Eslami and A. Biswas Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA Department of Mathematical Sciences, University of Tabriz, Tabriz, 51666-14766, Iran Department of Engineering Sciences, Faculty of Technol...

We derive a general theorem relating the energy and momentum with the velocity of any solitary wave solution of the generalized KdV equation in N -dimensions that follows from an action principle. Further, we show that our N -dimensional Lagrangian formulation leads to a subclass of the equations discussed recently by Rosenau, Hyman and Staley.

A new conservative finite difference scheme is presented for an initial-boundary value problem of the general Rosenau-RLW equation. Existence of its difference solutions are proved by Brouwer fixed point theorem. It is proved by the discrete energy method that the scheme is uniquely solvable, unconditionally stable, and second-order convergent. Numerical examples show the efficiency of the scheme.