Analytical description of stationary ideal MHD flows with constant total pressure

Incompressible stationary flows of ideal plasma are studied. By introduction of curvilinear system of coordinates in which streamlines and magnetic force lines form a family of coordinate surfaces, MHD equations are partially integrated and brought to a certain convenient form. It is demonstrated that the admissible group of Bogoyavlenskij's symmetry transformations (Bogoyavlenskij, 2001 [1]) performs as a scaling transformation (the scaling factor is an arbitrary function of one variable) for the curvilinear coordinates. Analytic description of stationary flows with constant total pressure is given. It is shown, that contact magnetic surfaces of such flows are translational surfaces, i.e. are swept out by translating one curve rigidly along another curve. Examples of solutions with constant total pressure possessing an arbitrariness in one function of two variables and three functions of one variable are given.