On the Periodic Cauchy Problem for the μ‐Modified Camassa‐Holm‐Novikov Type Equation

ABSTRACT This paper delves into the intricate periodic Cauchy problem associated with the ‐modified Camassa‐Holm‐Novikov equation. We first rigorously demonstrate that the occurrence of blow‐up phenomena in this equation is exclusively manifested through the formation of breaking waves and elucidate a comprehensive wave‐breaking mechanism of the solutions under certain initial data conditions. Subsequently, the existence of peaked travelling wave solutions is established, thereby enriching the understanding of the dynamical behavior of this remarkable equation. Finally, it is shown that the data‐to‐solution map is Hölder continuous in the , with .