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Explicit multipeakon solutions of Novikovs cubically nonlinear integrable Camassa-Holm type equation
University of Kent.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0003-4137-8272
University of Saskatchewan.
2009 (English)In: DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, ISSN 1548-159X, Vol. 6, no 3, 253-289 p.Article in journal (Refereed) Published
Abstract [en]

Recently Vladimir Novikov found a new integrable analogue of the Camassa-Holm equation which has nonlinear terms that are cubic, rather than quadratic, and which admits peaked soliton solutions (peakons). In this paper, the explicit formulas for multipeakon solutions of Novikovs cubically nonlinear equation are calculated, using the matrix Lax pair found by Hone and Wang. By a transformation of Liouville type, the associated spectral problem is related to a cubic string equation, which is dual to the cubic string that was previously found in the work of Lundmark and Szmigielski on the multipeakons of the Degasperis-Procesi equation.

Place, publisher, year, edition, pages
2009. Vol. 6, no 3, 253-289 p.
Keyword [en]
Peakons, cubic string, Novikovs equation, Degasperis-Procesi equation, distributional Lax pair, sum of minors
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-51597OAI: oai:DiVA.org:liu-51597DiVA: diva2:275951
Available from: 2009-11-09 Created: 2009-11-09 Last updated: 2013-11-14

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Lundmark, Hans

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