Symmetry reduction method and surfaces in life algebras for nonlinear phenomena in physics

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The proposed research concentrates on analytical methods for solving systems of nonlinear PDEs which appear in various branches of Mathematical Physics. The subject of this investigation involves symmetry reduction methods and geometric methods based on the analysis of surfaces immersed in Lie algebras. Certain applications to the equations of nonlinear field theory and fluid dynamics will be studied. The development of these methods provides us with new tools for dealing with nonlinear phenomena in physics, especially the ones which are described by multidimensional systems of PDEs and which so far have not been approached successfully by other methods. This program includes the following projects: