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Contribution to the Theory of Undular Bores

A journey around the Korteweg-de Vries equation

 With the support of EDFWater Monographs 


By Damien Violeau

Published: June 2022     

ISBN (electronic): 978-90-824846-9-4

ISBN (printed): 978-90-832612-0-1


The mission of Contribution to the Theory of Undular Bores. A journey around the Korteweg—de Vries equation is to describe some of the most important and classic theoretical features of undular bores, with the aim of enabling an engineer (or a non-specialist researcher) to journey through this beautiful topic of mathematical physics.Undular bores are water-surface oscillations that propagate between two levels of stationary water. They occur under various circumstances (such as tides, tsunamis, river dams and lock operations) and are a visible part of a larger group of physical phenomena termed dispersive shock waves. Readers will learn in a rigorous way but without difficult mathematical concepts, the theoretical developments that begun at the end of 19th century


Licencia de Creative Commons

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About this Water Monograph

Damien Violeau

Damien Violeau was educated at Ecole des Ponts (literally, the ‘School of Bridges’), one of the most prestigious French scientific educational institutes, where he is now full professor. Also, he is a senior Research engineer at EDF, one of the biggest energy companies in the world. His main fields of interest are free-surface flows, turbulent flows, numerical simulation, coastal protection and river-water works. In 2015, he was awarded Arthur T. Ippen award by IAHR.



«This is a very interesting book on the computations of undular bores using the Korteweg—de Vries equation. The author is right in stating that the mathematical apparatus for the solution of this approach is not well known in hydraulic engineering, given that it mainly was developed by mathematicians and physicists working on ocean dynamics. From this perspective, I think it is a welcome idea to present this material under the umbrella of IAHR, thereby making it accessible to hydraulic engineers»

Oscar Castro-Orgaz


«The raison d’être of this text is obvious: it is written simply in an accessible and clear language. There are very few texts within the mathematical literature which could compete with the present manuscript in terms of clarity. The exposition is wonderfullly pedagogical, but this is unsurprising if you ever had the opportunity to listen to Prof. Violeau’s lectures»

Denys Dutykh



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