On the peakon dynamical system of the second flow in the Camassa-Holm hierarchy

The Camassa-Holm hierarchy can be regarded as isospectral flows of the inhomogeneous string. This paper is devoted to the exploration of the second flow in the Camassa-Holm hierarchy (2ndCH) together with its peakon dynamical system as well as their nonisospectral generalizations. It is shown that a reduction of the peakon dynamical system of the 2ndCH equation results in the two-component modified Camassa- Holm (2mCH) interlacing peakon dynamical system. This reduction result is then extended to the nonisospectral case. More precisely, a nonisospectral extension of the 2ndCH is proposed together with its multipeakons based on classical determinant technique. It is also demonstrated that the corresponding peakon dynamical system can be reduced to the generalized nonisospectral 2mCH interlacing peakon dynamical system. Moreover, a special case of the proposed equation is investigated and a new phenomenon of 2-peakon is observed. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.