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arXiv · 1805.03323

Remarks on certain two-component systems with peakon solutions

Mike Hay·Andrew N. W. Hone·Vladimir S. Novikov·Jing Ping Wang
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Abstract

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.

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Mike Hay, Andrew N. W. Hone, Vladimir S. Novikov, Jing Ping Wang. 2018-05-09. Remarks on certain two-component systems with peakon solutions. https://arxiv.org/abs/1805.03323

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