Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913491998212096 |
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| author | Ivanov, Rossen I. |
| author_facet | Ivanov, Rossen I. |
| contents | A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to a KdV approximation with higher order nonlinearities and dispersion (higher-order KdV-type equation, or HKdV). The HKdV is related to the known integrable PDEs with an explicit nonlinear and nonlocal transformation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_03091 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability Ivanov, Rossen I. Exactly Solvable and Integrable Systems 76B15, 35Q35 A single incompressible, inviscid, irrotational fluid medium bounded above by a free surface is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to a KdV approximation with higher order nonlinearities and dispersion (higher-order KdV-type equation, or HKdV). The HKdV is related to the known integrable PDEs with an explicit nonlinear and nonlocal transformation. |
| title | Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability |
| topic | Exactly Solvable and Integrable Systems 76B15, 35Q35 |
| url | https://arxiv.org/abs/2409.03091 |