Asymptotic analysis of steady solutions of the KdVB equation with application to resonant sloshing |
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| Authors: | D E Amundsen E A Cox M P Mortell |
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| Institution: | (1) School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada;(2) School of Mathematical Sciences, University College Dublin, Dublin, Ireland;(3) Department of Applied Mathematics, University College Cork, Cork, Ireland |
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| Abstract: | The forced Korteweg-de Vries equation with Burgers’ damping (fKdVB) on a periodic domain, which arises as a model for water
waves in a shallow tank with forcing near resonance, is considered. A method for construction of asymptotic solutions is presented,
valid in cases where dispersion and damping are small. Through variation of a detuning parameter, families of resonant solutions
are obtained providing detailed insight into the resonant response character of the system and allowing for direct comparison
with the experimental results of Chester and Bones (1968). |
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| Keywords: | 35Q53 |
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