On the modelling of short and intermediate water waves

Rossen I. Ivanov

doi:10.1016/j.aml.2023.108653

On the modelling of short and intermediate water waves

Rossen I. Ivanov

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV equation. The Hamiltonian approach is employed in the derivation of a model equation in evolutionary form, which is both nonlinear and nonlocal, and most likely not integrable. Possible implications for the numerical solutions are discussed.

Original language	English
Article number	108653
Journal	Applied Mathematics Letters
Volume	142
DOIs	https://doi.org/10.1016/j.aml.2023.108653
Publication status	Published - Aug 2023

Keywords

Intermediate waves
Nonlinear waves
Nonlocal differential equations
Short waves

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10.1016/j.aml.2023.108653

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abstract = "The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV equation. The Hamiltonian approach is employed in the derivation of a model equation in evolutionary form, which is both nonlinear and nonlocal, and most likely not integrable. Possible implications for the numerical solutions are discussed.",

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AB - The propagation of water waves of finite depth and flat bottom is studied in the case when the depth is not small in comparison to the wavelength. This propagation regime is complementary to the long-wave regime described by the famous KdV equation. The Hamiltonian approach is employed in the derivation of a model equation in evolutionary form, which is both nonlinear and nonlocal, and most likely not integrable. Possible implications for the numerical solutions are discussed.

KW - Intermediate waves

KW - Nonlinear waves

KW - Nonlocal differential equations

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JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

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On the modelling of short and intermediate water waves

Abstract

Keywords

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