  Equations of magneto-gasdynamics in the natural curvilinear system of
coordinates where trajectories and magnetic lines play a role of coordinate
curves are reduced to the nonlinear vector wave equation coupled with the
incompressibility condition in the form of the generalized Cauchy integral. The
symmetry group of obtained equation, equivalence transformation, and group
classification with respect to the constitutive equation are calculated. New
exact solutions with functional arbitrariness describing non-stationary
incompressible flows with constant total pressure are given by explicit
formulae. The corresponding magnetic surfaces have the shape of deformed nested
cylinders, tori, or knotted tubes.
