Natural Hazards and Earth System Science www.nat-hazards-earth-syst-sci.net 1561-8633 1684-9981 7 1 2007 10.5194/nhess-7-33-2007 http://www.nat-hazards-earth-syst-sci.net/7/33/2007/ http://www.nat-hazards-earth-syst-sci.net/7/33/2007/nhess-7-33-2007.html http://www.nat-hazards-earth-syst-sci.net/7/33/2007/nhess-7-33-2007.pdf 33 40 2007-01-15 Extremal periodic wave profiles E. van Groesen groesen@math.utwente.nl Andonowati Department of Applied Mathematics, University of Twente, The Netherlands LabMath-Indonesia, Bandung, Indonesia Department of Mathematics, Institut Teknologi Bandung, Indonesia As a contribution to deterministic investigations into extreme fluid surface waves, in this paper wave profiles of prescribed period that have maximal crest height will be investigated. As constraints the values of the momentum and energy integrals are used in a simplified description with the KdV model. The result is that at the boundary of the feasible region in the momentum-energy plane, the only possible profiles are the well known cnoidal wave profiles. Inside the feasible region the extremal profiles of maximal crest height are "cornered" cnoidal profiles: cnoidal profiles of larger period, cut-off and periodically continued with the prescribed period so that at the maximal crest height a corner results. Olagnon, M. and Prevosto, M. (Eds.): Proceedings Rogue Waves 2004, Ifremer, ISBN 2-84433-150-5, 2004. Proceedings Rogue Waves: Edinburgh, Scotland, 2005, http://www.icms.org.uk/meetings/2005/roguewaves/index.html, 2005. van Groesen, E. and de Jager, E. M.: Mathematical structures in continuous dynamical systems, North Holland, Elsevier, Amsterdam, 1994. \bibitem[Van Groesen and Andonowati(2006a)] GroAan06FinEn van Groesen, E. and Andonowati: Finite energy wave signals of extremal amplitude in the spatial NLS-dynamics, Phys. Lett. A, 357, 86–91, 2006.