TY - JOUR
T1 - A study of wave trapping between two obstacles in the forced Korteweg–de Vries equation
AU - Kim, Hongjoong
AU - Choi, Heesun
N1 - Funding Information:
This research of Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2014R1A1A2058271). We thank the editors and the anonymous reviewers for their constructive comments that greatly improved the manuscript.
PY - 2018/2/1
Y1 - 2018/2/1
N2 - In the forced Korteweg–de Vries equation, a trail of waves can be temporarily trapped between two bumps. Wave propagations vary depending on the solution types and the form of the bumps. In this paper, we study the propagation tendencies of these temporarily trapped waves and especially consider the solitary and flat top solutions over the bumps of different distances and heights. A concept of energy related to wave speeds is defined in the region between the bumps, and it turns out that the trapped waves have to overcome a certain threshold of energy in order to escape out of the region. The numerical investigations are focused on the influence of the distance and the height of the bumps on the energy barrier.
AB - In the forced Korteweg–de Vries equation, a trail of waves can be temporarily trapped between two bumps. Wave propagations vary depending on the solution types and the form of the bumps. In this paper, we study the propagation tendencies of these temporarily trapped waves and especially consider the solitary and flat top solutions over the bumps of different distances and heights. A concept of energy related to wave speeds is defined in the region between the bumps, and it turns out that the trapped waves have to overcome a certain threshold of energy in order to escape out of the region. The numerical investigations are focused on the influence of the distance and the height of the bumps on the energy barrier.
KW - Forced Korteweg–de Vries equation
KW - Temporarily trapped waves
KW - Threshold condition
KW - Two bumps
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U2 - 10.1007/s10665-017-9919-5
DO - 10.1007/s10665-017-9919-5
M3 - Article
AN - SCOPUS:85025476660
SN - 0022-0833
VL - 108
SP - 197
EP - 208
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
IS - 1
ER -