Holm, Darryl D. and Hone, Andrew N.W. (2005) A class of equations with peakon and pulson solutions (with an Appendix by Harry Braden and John ByattSmith). Journal of Nonlinear Mathematical Physics, 12 (Sup.1). pp. 380394. ISSN 14029251. (Full text available)
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Official URL http://staff.www.ltu.se/~norbert/home_journal/elec... 
Abstract
We consider a family of integrodifferential equations depending upon a parameter b as well as a symmetric integral kernel g(x). When b=2 and g is the peakon kernel (i.e. g(x)=exp(?x) up to rescaling) the dispersionless CamassaHolm equation results, while the DegasperisProcesi equation is obtained from the peakon kernel with b=3. Although these two cases are integrable, generically the corresponding integroPDE is nonintegrable. However,for b=2 the family restricts to the pulson family of Fringer & Holm, which is Hamiltonian and numerically displays elastic scattering of pulses. On the other hand, for arbitrary b it is still possible to construct a nonlocal Hamiltonian structure provided that g is the peakon kernel or one of its degenerations: we present a proof of this fact using an associated functional equation for the skewsymmetric antiderivative of g. The nonlocal bracket reduces to a noncanonical Poisson bracket for the peakon dynamical system, for any value of b?1.
Item Type:  Article 

Subjects: 
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations Q Science > QA Mathematics (inc Computing science) > QA801 Analytic mechanics 
Divisions:  Faculties > Sciences > School of Mathematics Statistics and Actuarial Science 
Depositing User:  Andrew N W Hone 
Date Deposited:  21 Jun 2014 22:46 UTC 
Last Modified:  27 Jun 2017 16:21 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/41497 (The current URI for this page, for reference purposes) 
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