Variational derivation of KdVtype of models for surface water waves
Groesen, E. van and Andonowati (2007) Variational derivation of KdVtype of models for surface water waves. Physics Letters A, 366 (3). pp. 195201. ISSN 03759601
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Abstract:  Using the Hamiltonian formulation of surface waves, we approximate the kinetic energy and restrict the governing generalized action principle to a submanifold of unidirectional waves. Different from the usual method of using a series expansion in parameters related to wave height and wavelength, the variational methods retains the Hamiltonian structure (with consequent energy and momentum conservation) and makes it possible to derive equations for any dispersive approximation. Consequentially, the procedure is valid for waves above finite and above infinite depth, and for any approximation of dispersion, while quadratic terms in the wave height are modeled correctly. For finite depth this leads to higherorder KdV type of equations with terms of different spatial order. For waves above infinite depth, the pseudodifferential operators cannot be approximated by finite differential operators and all quadratic terms are of the same spatial order.

Item Type:  Article 
Copyright:  © 2007 Elsevier Science 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
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Link to this item:  http://purl.utwente.nl/publications/61745 
Official URL:  http://dx.doi.org/10.1016/j.physleta.2007.02.031 
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