We study the error propagation of time integrators of solitary wave solutions for the regularized long wave equation, ut +ux+ 2 (u)x −uxxt = 0, by using a geometric interpretation of these waves as relative equilibria. We show that the error growth is linear for schemes that preserve invariant quantities of the problem and quadratic for ‘nonconservative’ methods. Numerical experiments are prese...

Stable and Unstable Solitary-Wave Solutions of the Generalized Regularized Long-Wave Equation J. L. Bona,1 W. R. McKinney,2 and J. M. Restrepo3,∗ 1 Department of Mathematics and Texas Institute for Computational and Applied Mathematics, University of Texas, Austin, TX 78712, USA 2 Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA 3 Mathematics Department and Pro...

This paper obtains solitary waves, shock waves and singular solitons alon with conservation laws of the Rosenau Kortewegde Vries regularized long wave (R-KdV-RLW) equation with power law nonlinearity that models the dynamics of shallow water waves. The ansatz approach and the semi-inverse variational principle are used to obtain these solutions. The constraint conditions for the existence of so...

It is shown that the regularized long-wave equation admits a family of solitary waves of depression. Some of these solitary waves are stable while others are unstable. The proof of stability and instability is based on the general theory of Grillakis, Shatah and Strauss. The results are illustrated by numerical simulation using a spectral discretization.

The Modified Regularized Long Wave (MRLW) equation is solved numerically by Adomian decomposition method (ADM) with some initial conditions. The method leads to high accurate and efficient results. Three polynomial invariant conditions are evaluated to determine the conservation properties of the problem. The convergence of Adomian decomposition method applied to the MRLW equation is proved. Mo...