Math @ Duke

Publications [#300222] of JianGuo Liu
Papers Published
 Chertock, A; Liu, JG; Pendleton, T, Elastic collisions among peakon solutions for the CamassaHolm equation,
Applied Numerical Mathematics, vol. 93
(January, 2015),
pp. 3046, ISSN 01689274 [doi]
(last updated on 2018/03/24)
Abstract: © 2014 IMACS. The purpose of this paper is to study the dynamics of the interaction among a special class of solutions of the onedimensional CamassaHolm equation. The equation yields soliton solutions whose identity is preserved through nonlinear interactions. These solutions are characterized by a discontinuity at the peak in the wave shape and are thus called peakon solutions. We apply a particle method to the CamassaHolm equation and show that the nonlinear interaction among the peakon solutions resembles an elastic collision, i.e., the total energy and momentum of the system before the peakon interaction is equal to the total energy and momentum of the system after the collision. From this result, we provide several numerical illustrations which support the analytical study, as well as showcase the merits of using a particle method to simulate solutions to the CamassaHolm equation under a wide class of initial data.


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