The governing equations for waves propagating in water are derived by use of conservation laws. The equations are then cast onto dimensionless form and two important parameters are obtained. Approximations by use of asymptotic expansions in one or both of the parameters are then applied on the governing equations and we show that several different completely integrable equations, with different scaling transformations and at different order of approximations, can be derived. More precisely, the Korteweg-de Vries, Kadomtsev-Petviashvili and Boussinesq are obtained at first order, while the Camassa-Holm, Degasperis-Procesi, nonlinear Schrödinger and the Davey-Stewartson equations are obtained at second order. We discuss shortly some of the properties for each of the obtained equations.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:ntnu-9888 |
| Date | January 2009 |
| Creators | Jansen, Arne Kristian |
| Publisher | Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, Institutt for matematiske fag |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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