Splitting phenomenon of a higher-order shallow water theory associated with a longitudinal planetary waves

- A higher order approximation for the Cauchy-Poisson free boundary problem associated with a nonstationary motion of a perfect incompressible fluid circulating around the equatorial plane of a planet is considered.
- It is shown that the above free boundary problem admits two functionally independent systems, while the classical problem for the flat bottom admits only one system.
- Additionally, the singular exact solutions are provided for the exact mathematical model describing the above longitudinal planetary waves.

The Cauchy-Poisson free boundary problem associated with a nonstationary motion of a perfect incompressible fluid circulating around the equatorial plane of a planet is considered. It is shown that the corresponding theory of a higher-order shallow approximation admits two functionally independent systems, while the classical problem for the flat bottom admits only one system.