This article is cited in 5 papers

Numerical study of Peakons and $k$-Solitons of the Camassa–Holm and Holm–Hone equations

S. P. Popov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia

Abstract: The spectral Fourier and Runge–Kutta methods are used to study the Camassa–Holm and Holm–Hone equations numerically. Numerical results for problems with initial data leading to the generation and interaction of peakons and $k$-solitons are discussed.

Key words: Camassa–Holm equation, Holm–Hone equation, $k$-soliton, peakon, $k$-cuspon.

UDC: 519.634

Received: 29.12.2009
Revised: 28.10.2010

 English version: Computational Mathematics and Mathematical Physics, 2011, 51:7, 1231–1238

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