Unified formulation for stationary polytropes with stellar winds and development of a numerical scheme to obtain their structures

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We have found a new formulation in which axisymmetric and stationary states of barotropic stars with magnetic fields are easily handled. This has been done by considering the integrability condition among the basic equations. This integrability condition results in the general form for the current density. By applying this formulation we have developed a numerical scheme that could be used to obtain many stationary configurations with magnetic fields which are found by this scheme for the firt time in the world. At the same time, this formulation could be applied to obtain stellar wind solutions which have not been fully analyzed yet. By using this scheme, completely new analytic solutions for triaxial configurations and prolate ellipsoidal stationary structures have also been obtained..