Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion

Congy, Thibault, Ivanov, S. K., Kamchatnov, A. M. and Pavloff, N. (2017) Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27 (8). 083107. ISSN 1054-1500

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Official URL: https://doi.org/10.1063/1.4997052

Abstract

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this “Kaup-Boussinesq model” for which a flat water surface is modulationally stable, we speak below of “positive dispersion” model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks, which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

Item Type: Article
Subjects: F300 Physics
G100 Mathematics
H800 Chemical, Process and Energy Engineering
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Elena Carlaw
Date Deposited: 30 Nov 2020 13:03
Last Modified: 30 Nov 2020 13:15
URI: http://nrl.northumbria.ac.uk/id/eprint/44864

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