Benjamin-Ono model of an internal wave under a flat surface

Alan Compelli; Rossen Ivanov

doi:10.3934/dcds.2019185

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2019, Volume 39, Issue 8: 4519-4532. Doi: 10.3934/dcds.2019185

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Benjamin-Ono model of an internal wave under a flat surface

Alan Compelli^1, and
Rossen Ivanov^2,

1.
School of Mathematical Sciences, University College Cork, Cork, Ireland
2.
School of Mathematical Sciences, Technological University Dublin, City Campus, Kevin Street, Dublin 8, Ireland

The paper is for the special theme: Mathematical Aspects of Physical Oceanography, organized by Adrian Constantin.

Received: July 31, 2018

Revised: September 30, 2018

Published: May 2019

This work was supported by EPSRC grant no EP/K032208/1. AC is also funded by SFI grant 13/CDA/2117

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Abstract

A two-layer fluid system separated by a pycnocline in the form of an internal wave is considered. The lower layer is infinitely deep, with a higher density than the upper layer which is bounded above by a flat surface. The fluids are incompressible and inviscid. A Hamiltonian formulation for the dynamics in the presence of a depth-varying current is presented and it is shown that an appropriate scaling leads to the integrable Benjamin-Ono equation.

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Mathematics Subject Classification: Primary: 35Q35, 35Q51, 35Q53; Secondary: 37K10.

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Figure 1. The system under study

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References

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