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Vortices, circumfluence, symmetry groups and Darboux transformations of the Euler equations | | S. Y. Lou
; X. Y. Tang
; M. Jia
; F. Huang
; | | Date: |
23 Sep 2005 | | Subject: | Pattern Formation and Solitons; Adaptation and Self-Organizing Systems | nlin.PS nlin.AO | | Abstract: | The Euler equation (EE) is one of the basic equations in many physical fields such as the fluids, plasmas, condense matters, astrophysics, oceanic and atmospheric dynamics. A new symmetry group theorem of the two dimensional EE is obtained via a simple direct method and the theorem is used to find em exact analytical
m vortex and circumfluence solutions. Some types of Darboux transformations (DTs) for the both two and three dimensional EEs are obtained for em arbitrary spectral parameters
m which indicates that the EEs are integrable and the Navier-Stockes (NS) equations with large Renoyed number are nearly integrable, i.e, they are singular perturbations of the integrable EEs. The possibility of the vortex and circumfluence solutions to approximately explain the tropical cyclones (TCs), especially, the Hurricane Andrew 1992, is discussed. | | Source: | arXiv, nlin.PS/0509039 | | Services: | Forum | Review | PDF | Favorites | |
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