This article is cited in 2 papers

New compacton solutions of an extended Rosenau–Pikovsky equation

S. P. Popov

Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia

Abstract: The $\mathrm{K}(\cos^m, \cos^n)$ equation is proposed, which extends the Rosenau–Pikovsky $\mathrm{K}(\cos)$ 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 $\mathrm{K}(2,2)$ and $\mathrm{K}(\cos)$ equations. New types of peak-shaped compactons and kovatons of various amplitudes are found.

Key words: evolution equations of mathematical physics, KdV equation, $\mathrm{K}(m,n)$ equation, Rosenau–Hyman equation, $\mathrm{K}(\cos)$ equation, Rosenau–Pikovsky equation, compacton, kovaton, soliton, kink, multisoliton interaction.

UDC: 519.634

Received: 17.04.2016
Revised: 22.11.2016

DOI: 10.7868/S0044466917090101

 English version: Computational Mathematics and Mathematical Physics, 2017, 57:9, 1540–1549

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