New compacton solutions of an extended Rosenau–Pikovsky equation

Resumo

The K(cos^m, cosⁿ) equation is proposed, which extends the Rosenau–Pikovsky K(cos) equation to the case of power-law dependence of nonlinearity and dispersion. The properties of compacton and kovaton solutions are numerically studied and compared with solutions of the K(2,2) and K(cos) equations. New types of peak-shaped compactons and kovatons of various amplitudes are found.