STEADY STATE SOLUTIONS OF THE FORCED KORTEWEG-DE VRIES EQUATION OVER COSINUSOIDAL TOPOGRAPHIES WITH TWO SPATIAL WAVENUMBERS
In this thesis, the free surface flow over a spatially wavy bottom is analysed using the stationary fKdV (forced Korteweg-De Vries) equation. In particular, perturbations to the uniform, solitary, and cnoidal solutions due to a bottom sinusoidal topography with 2 spatial wavenumbers are studied u...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/76177 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | In this thesis, the free surface flow over a spatially wavy bottom is analysed using the
stationary fKdV (forced Korteweg-De Vries) equation. In particular, perturbations
to the uniform, solitary, and cnoidal solutions due to a bottom sinusoidal topography
with 2 spatial wavenumbers are studied using the fKdV equation. By asymptotic
analysis, it is shown that there are several types of near solitary solutions which
depends on the amplitudes and the wavenumbers of the topography. Furthermore,
several types of resonances may occur in the near cnoidal solution due to the interaction
between the 2 topography’s wavenumbers. This analysis is shown to be
consistent with the numerical results. The solution structure to these perturbations
is also analyzed by calculating the bifurcation diagrams using pseudo arclength
numerical continuation. |
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