Trapped depression solitary waves for the forced fifth-order forced Korteweg-de Vries equation

Marcelo V. Flamarion, Roberto Ribeiro

Resumo


In this work, we investigate numerically trapped depression solitary waves in gravity-capillary flows for the fifth-order forced Korteweg-de Vries equation. We compute depression solitary waves with a single local minimum and three local minima that remain trapped bouncing back and forth between two topographic obstacles for large times. Besides, we study the wave stability of these trapped waves by disturbing their amplitudes. The depression solitary wave with a single local minimum is stable, whereas the one with three local minima splits into several depression solitary waves after a series of rebounds between the obstacles.


Palavras-chave


Gravity-capillary waves;Solitary waves;Trapped waves

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Referências


M.V. Flamarion. “Generation of trapped depression solitary waves in gravity-capillary flows over an obstacle”. In: Computational and Applied Mathematics 41 (2022), pp. 1–9. doi: 10.1007/s40314-021-01734-w.

M.V. Flamarion, Milewski P. A., and A. Nachbin. “Rotational waves generated by currenttopography interaction”. In: Studies in Applied Mathematics 142 (2019), pp. 433–464. doi: doi.org/10.1111/sapm.12253.

M.V. Flamarion and R. Ribeiro-Jr. “Gravity-capillary flows over obstacles for the fifth-order forced Korteweg-de Vries equation”. In: Journal of Engineering Mathematics 129 (2021), pp. 1–10. doi: 10.1007/s10665-021-10153-z.

M.V. Flamarion and R. Ribeiro-Jr. “Gravity-capillary wave interactions generated by moving disturbances: Euler equations framework”. In: Journal of Engineering Mathematics 132 (2022), pp. 1–10. doi: 10.1007/s10665-021-10207-2.

R. Grimshaw and M. Malewoong. “Transcritical flow over obstacles and holes: forced Kortewegde Vries framework”. In: Journal of Fluid Mechanics 881 (2019), pp. 660–678. doi: 10.1017/jfm.2019.767.

H. Kim and H. Choi. “A study of wave trapping between two obstacles in the forced Kortewegde Vries equation”. In: Journal of Engineering Mathematics 108 (2017), pp. 197–208. doi: 10.1007/s10665-017-9919-5.

S. Lee. “Dynamics of Trapped Solitary Waves for the Forced KdV Equation”. In: Symmetry 21 (2018), pp. 467–490. doi: 10.3390/sym10050129.

S. Lee and S. Whang. “Trapped supercritical waves for the forced KdV equation with two bumps”. In: Applied Mathematical Modeling 39 (2015), pp. 2649–2660. doi: 10.1016/ j.apm.2014.11.007.

P. A. Milewski and J-M. Vanden-Broeck. “Time dependent gravity-capillary flows past an obstacle”. In: Wave Motion 29 (1999), pp. 63–79. doi: 10.1016/S0165-2125(98)00021-3.

L.N. Trefethen. Spectral Methods in MATLAB. Philadelphia: SIAM, 2001. isbn: 0898714656.

Y. Zhu. “Resonant generation of nonlinear capillary-gravity waves”. In: Physics of Fluids 7 (1995), pp. 2294–2296. doi: 10.1063/1.868479




DOI: https://doi.org/10.5540/03.2022.009.01.0313

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