Remarks on certain two-component systems with peakon solutions
Exactly Solvable and Integrable Systems
2018-05-10 v1 Mathematical Physics
Analysis of PDEs
math.MP
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 , 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 . 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.
Cite
@article{arxiv.1805.03323,
title = {Remarks on certain two-component systems with peakon solutions},
author = {Mike Hay and Andrew N. W. Hone and Vladimir S. Novikov and Jing Ping Wang},
journal= {arXiv preprint arXiv:1805.03323},
year = {2018}
}