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Remarks on certain two-component systems with peakon solutions

Hay, M., Hone, Andrew N.W., Novikov, Vladimir S., Wang, Jing Ping (2019) Remarks on certain two-component systems with peakon solutions. Journal of Geometric Mechanics, 11 (4). pp. 561-573. ISSN 1941-4889. (doi:10.3934/jgm.2019028) (KAR id:67146)

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We consider a Lax pair found by Xia, Qiao and Zhou for a family of two-component analogues of the Camassa-Holm equation, including an arbitrary function H, and show that this apparent freedom can be removed via a combination of a reciprocal transformation and a gauge transformation, which reduces the system to triangular form. The resulting triangular system may or may not be integrable, depending on the choice of H. In addition, we apply the formal series approach of Dubrovin and Zhang to show that scalar equations of Camassa-Holm type with homogeneous nonlinear terms of degree greater than three are not integrable. This article is dedicated to Darryl Holm on his 70th birthday.

Item Type: Article
DOI/Identification number: 10.3934/jgm.2019028
Subjects: Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Jing Ping Wang
Date Deposited: 27 May 2018 22:32 UTC
Last Modified: 16 Feb 2021 13:55 UTC
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