Nonexistence of periodic peakon and peakon for a highly nonlinear shallow-water model

In this paper, we investigate the nonexistence of the periodic peakon and peakon for a highly nonlinear shallow-water model, which has been recently derived from the full governing equations for two dimensional flow with the Coriolis effect or with constant vorticity, under a larger scaling than the Camassa-Holm (CH) one. Note that the so obtained model not only has CH-type terms, but also exhibits cubic order nonlinearities. Thus it is interesting to study how the higher power nonlinear terms affect the existence of the (periodic) peakon.