| Issue |
Math. Model. Nat. Phenom.
Volume 13, Number 2, 2018
Shock Waves, Discontinuities and Singularities in Natural Phenomena
|
|
|---|---|---|
| Article Number | 19 | |
| Number of page(s) | 22 | |
| DOI | https://doi.org/10.1051/mmnp/2018021 | |
| Published online | 17 May 2018 | |
Invariant solutions and shock atmospheric waves in a thin circular layer
1
Center ALGA, Department of Mathematics and Natural Sciences, Blekinge Institute of Technology,
Karlskrona, Sweden
2
Department of Mathematics and Physics, University of Wisconsin-Parkside,
Kenosha, USA
3
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences,
Moscow, Russia
* Corresponding author: ibragimo@uwp.edu
Received:
5
October
2017
Accepted:
6
October
2017
The objective of this paper is to investigate the nonlinear mathematical model describing equatorial waves from Lie group analysis point of view in order to understand the nature of shallow water model theory, which is associated to planetary equatorial waves. Such waves correspond to the Cauchy–Poisson free boundary problem on the nonstationary motion of a perfect incompressible fluid circulating around a solid circle of a large radius.
Mathematics Subject Classification: 35C99 / 70S10 / 70G65
Key words: Method of conservation laws / nonlinear PDEs / symmetries / exact solutions / chaplygin gas
© EDP Sciences, 2018
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