Whitfield, AJ;
Johnson, ER;
(2015)
Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation.
Physical Review E: statistical, nonlinear, and soft matter physics
, 91
(5)
, Article 051201. 10.1103/PhysRevE.91.051201.
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Abstract
The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. There is currently no entirely satisfactory explanation as to why these wave packets form. Here the initial value problem is considered within the context of the Gardner-Ostrovsky, or rotation-modified extended Korteweg-de Vries, equation. The linear Gardner-Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. It is found here that a nonlinear splitting of the wave-number spectrum at the zero-dispersion point, where energy is shifted into the modulationally unstable regime of the Gardner-Ostrovsky equation, is responsible for the wave-packet formation. Numerical comparisons of the decay of a solitary wave in the Gardner-Ostrovsky equation and a derived nonlinear Schrödinger equation at the zero-dispersion point are used to confirm the spectral splitting.
| Type: | Article |
|---|---|
| Title: | Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation. |
| Location: | United States |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1103/PhysRevE.91.051201 |
| Publisher version: | http://dx.doi.org/10.1103/PhysRevE.91.051201 |
| Language: | English |
| Additional information: | ©2015 American Physical Society |
| Keywords: | 47.35.Fg, 92.10.Ei, 92.10.Hm, 42.65.−k |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1474256 |
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