The purpose of the research was to investigate the exact solutions of nonlinear shallow water equations associated with planetary equatorial waves corresponding to the Cauchy-Poisson free boundary problem describing the nonstationary motion of an incompressible perfect fluid propagating around a solid circle. We consider water waves for which the ratio of the depth of fluid above the circular bottom to the radius of the circle is small (shallow water).
Ibragimov, R. , Mongrain, L. , Stimmel, B. , Trozkaya, O. , Lin, G. , Zhang, S. , Vatchev, V. and Stankiewicz, D. (2021) Visualization of Exact Invariant Solutions Associated with Atmospheric Waves in a Thin Circular Layer. Journal of Applied Mathematics and Physics, 9, 901-919. https://doi.org/10.4236/jamp.2021.95061
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Journal of Applied Mathematics and Physics