We study the properties of compacton-anticompacton collision processes. We compare and contrast results for the case of compacton-anticompacton solutions of the K(l,p) Rosenau-Hyman (RH) equation for l = p = 2, with compacton-anticompacton solutions of the L(l,p) Cooper-Shepard-Sodano (CSS) equation for p = 1 and l = 3. This study is performed using a Padé discretization of the RH and CSS equat...

Extending a Padé approximant method used for studying compactons in the Rosenau-Hyman (RH) equation, we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS equation has a conserved Hamiltonian which has allowed various approaches for studying analytically the nonlinear stability of the solutions. We study three ...

Zero curvature formulations are given for the “dual hierarchies” of standard soliton equation hierarchies, recently introduced by Olver and Rosenau, including the physically interesting Fuchssteiner-Fokas-CamassaHolm hierarchy. PACS Numbers: 03.40.Kf, 47.20.Ky, 52.35.Sb Through the years since the discovery of the notion of “integrability” in PDEs, quite a number of integrable PDEs have been di...

The numerical simulation of the propagation of nonlinear waves may present numericallyinduced radiation. Compactons, solitary waves with compact support, are no exception. The numerical radiation generated by compactons of the Rosenau-Hyman K(2, 2) equation calculated by means of a fourth-order finite element method is illustrated. Small-amplitude forward and backward radiation are shown in the...

In this paper, we first consider the Rosenau equation with quadratic nonlinearity and identify its Lie symmetry algebra. We obtain reductions of to ODEs, find periodic analytical solutions in terms elliptic functions. Then, considering a general power-type nonlinearity, prove non-existence solitary waves for some parameters using Pohozaev type identities. The Fourier pseudo-spectral method is p...

A numerical study of the nonlinear wave solutions of the Rosenau-Pikovsky K(cos) equation is presented. This equation supports at least two kind of solitary waves with compact support: compactons of varying amplitude and speed, both bounded, and kovatons which have the maximum compacton amplitude, but arbitrary width. A new Padé numerical method is used to simulate the propagation and, with sma...