The generalized regularized long-wave equation admits a family of negative solitary waves. The stability of these waves is investigated by numerical simulation using a spectral discretization. © 2009 IMACS. Published by Elsevier B.V. All rights reserved.

Abstract: In this paper, we demonstrate the effectiveness of the (G ′ G )-expansion method by seeking more exact solutions of the SRLW equation, the (2+1) dimensional PKP equation and the (3+1) dimensional potential-YTSF equation. By the method, the two nonlinear evolution equations are separately reduced to non-linear ordinary differential equations (ODE) by using a simple transformation. As a...

In this paper the Variational Iteration Method (VIM) is used to investigate the damped generalized regularized long-wave equation(DGRLW). The solution of the nonlinear DGRLW equation is calculated in the form of series with computable components. Numerical examples are tested to illustrate the proposed scheme. Moreover, the approximate solutions are compared with the exact solutions.

The regularized long wave equation (RLW) is solved numerically by using the quintic B-spline Galerkin finite element method. The same method is applied to the time-split RLW equation. Comparison is made with both analytical solutions and some previous results. Propagation of solitary waves, interaction of two solitons are studied. © 2005 Elsevier B.V. All rights reserved. MSC: 65N30; 65D07; 76B25