ORCID
- Rossen I. Ivanov: 0000-0003-1008-8272
Abstract
In this paper, we derive a higher-order Korteweg–de Vries (HKdV) equation as a model to describe the unidirectional propagation of waves on an internal interface separating two fluid layers of varying densities. Our model incorporates underlying currents by permitting a sheared current in both fluid layers, and also accommodates the effect of the Earth's rotation by including Coriolis forces (restricted to the Equatorial region). The resulting governing equations describing the water wave problem in two fluid layers under a “flat-surface” assumption are expressed in a general form as a system of two coupled equations through Dirichlet–Neumann (DN) operators. The DN operators also facilitate a convenient Hamiltonian formulation of the problem. We then derive the HKdV equation from this Hamiltonian formulation, in the long-wave, and small-amplitude, asymptotic regimes. Finally, it is demonstrated that there is an explicit transformation connecting the HKdV we derive with the following integrable equations of a similar type: KdV5, Kaup–Kuperschmidt equation, Sawada–Kotera equation, and Camassa–Holm and Degasperis–Procesi equations.
Keywords
Camassa–Holm equation, Degasperis–Procesi equation, Dirichlet–Neumann operators, internal waves, Kaup–Kuperschmidt equation, KdV equation, KdV hierarchy, Sawada–Kotera equation, solitons
DOI Link
Publication Date
2024-01-01
Publication Title
Studies in Applied Mathematics
Volume
153
Issue
4
ISSN
0022-2526
Deposit Date
2025-08-01
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Additional Links
Recommended Citation
Henry, David; Ivanov, Rossen I.; and Sakellaris, Zisis N., "Higher-order integrable models for oceanic internal wave–current interactions" (2024). Research Outputs: 2025-Present. 2.
https://arrow.tudublin.ie/scschmatro/2