Abstract
The propagation of dispersive shock waves (DSWs) is investigated in the cylindrical Gardner (cG) equation, which is obtained by employing a similarity reduction to the two-space one-time (2+1) dimensional Gardner-Kadomtsev-Petviashvili (Gardner-KP) equation. We consider the steplike initial condition along a parabolic front. Then, the cG-Whitham modulation system, which is a description of DSW evolution in the cG equation, in terms of appropriate Riemann-type variables is derived. Our study is supported by numerical simulations. The comparison is given between the direct numerical solution of the cG equation and the DSW solution obtained from the numerical solution of the Whitham system. According to this comparison, a good agreement is found between the solutions.
| Original language | English |
|---|---|
| Article number | 052214 |
| Journal | Physical Review E |
| Volume | 102 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 23 Nov 2020 |
Bibliographical note
Publisher Copyright:© 2020 American Physical Society.
Funding
We would like to thank the referees for their constructive comments and recommendations. This research was supported by the Istanbul Technical University Office of Scientific Research Projects (ITU BAPSIS) under Grant No. TGA-2018-41318. We thank D. E. Baldwin for the MATLAB codes of the version of the ETDRK4 method that we use in the study.
| Funders | Funder number |
|---|---|
| ITU BAPSIS | TGA-2018-41318 |
| Istanbul Technical University Office of Scientific Research Projects |