Abstract
A forced Korteweg–de Vries (fKdV) equation can be used to model the surface wave of a two-dimensional water flow over a bump when the upstream Froude number is near one. The fKdV model typically has four types of solutions: sub-critical cnoidal waves, sub-critical hydraulic fall, transcritical upstream soliton radiation, and supercritical multiple solitary waves. This paper provides a numerical demonstration of the stability of the hydraulic falls and cnoidal waves solutions.
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Donahue, A.S., Shen, S.S.P. Stability of hydraulic fall and sub-critical cnoidal waves in water flows over a bump. J Eng Math 68, 197–205 (2010). https://doi.org/10.1007/s10665-010-9371-2
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DOI: https://doi.org/10.1007/s10665-010-9371-2