In this paper, by using a direct method based on the Jacobi elliptic functions, exact solutions of space-time fractional symmetric regularized long wave (SRLW) equation have been obtained. The function nonlinear ordinary differential (auxiliary) $\left({dF}/{d \xi}\right) ^{2} = PF^{4} (\xi)+QF^{2} (\xi) + R$ also examined. Besides, found in general form including rational, trigonometric and hy...

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...

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...

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...

We present a review of the normal form theory for weakly dispersive nonlinear wave equations where the leading order phenomena can be described by the KdV equation. This is an infinite dimensional extension of the well-known Poincaré-Dulac normal form theory for ordinary differential equations. We also provide a detailed analysis of the interaction problem of solitary waves as an important appl...

In this paper, a finite difference method for initial-boundary value problem of nonlinear Regularized-Long-Wave equation was considered. A energy conservative finite difference scheme of three levels was proposed, convergence and stability of difference solution was proved, if picking suitably,the accuracy of the new scheme is higher than others, so the method is efficient and reliable.

The BBM or Regularized Long Wave Equation is shown to possess only three non-trivial independent conservation laws. In order to prove this result, a new theory of Euler-type operators in the formal calculus of variations will be developed in detail.