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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
