SYMMETRIES OF PDEs SYSTEMS IN SOLAR PHYSICS AND CONTACT GEOMETRY

One considers a class of PDEs systems (1) equivalent to (8) and one determines the PDEs system (10) which defines the associated symmetry group. Particularly, for the Blair system (2)+(3) equivalent to (14), one finds the symmetry Lie group G (Theorem 5). One proves that the class of PDEs systems in the form (8)+(14′) which are invariant with respect to the Lie group G, is reduced to the Blair system (Theorem 6). One finds new solutions B (2) 1 and B (3) 1 of the Blair system, and thus new ”force-free” model of solar physics. Key-words: Blair system, infinitesimal symmetries, symmetry group, groupinvariant solutions. Mathematical Subject Classification: 58G35, 35A30 Physics Subject Classification: 96.60.H