Vortices, circumfluence, symmetry groups and Darboux transformations of the (2+1)-dimensional Euler equation

Abstract

The Euler equation (EE) is one of the basic equations in many physical fields such as fluids, plasmas, condensed matter, astrophysics, oceanic and atmospheric dynamics. A symmetry group theorem of the (2+1)-dimensional EE is obtained via a simple direct method which is thus utilized to find \em exact analytical \rm vortex and circumfluence solutions. A weak Darboux transformation theorem of the (2+1)-dimensional EE can be obtained for \em arbitrary spectral parameter \rm from the general symmetry group theorem. \rm Possible applications of the vortex and circumfluence solutions to tropical cyclones, especially Hurricane Katrina 2005, are demonstrated.

arXiv comment25 pages, 9 figures

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Cited by in corpus (2)

• Similarity reductions and new nonlinear exact solutions for the 2D incompressible Euler equations
• Extensions of the symmetry algebra and Lax representations for the two-dimensional Euler equation