Projects per year
The nonlinear Schrödinger (NLS) equation describes the modulational limit of many surface water wave problems. Dark solitary waves of the NLS equation asymptote to a constant in the far field and have a localized decrease to zero amplitude at the origin, corresponding to water wave solutions that asymptote to a uniform periodic Stokes wave in the far field and decreasing oscillations near the origin. It is natural to ask whether these dark solitary waves can be found in the irrotational Euler equations. In this paper, we find such solutions in the context of flexural-gravity waves, which are often used as a model for waves in ice-covered water. This is a situation in which the NLS equation predicts steadily travelling dark solitons. The solution branches of dark solitons are continued, and one branch leads to fully localized solutions at large amplitudes.
|Journal||Proceedings of the Royal Society A|
|Early online date||28 Nov 2012|
|Publication status||Published - Feb 2013|
FingerprintDive into the research topics of 'Steady dark solitary flexural gravity waves'. Together they form a unique fingerprint.
- 1 Finished
Nonlinear Hydroelastic Waves with Applications to Ice Sheets
Engineering and Physical Sciences Research Council
12/11/12 → 11/11/15
Project: Research council