Progress in classically solving ten-dimensional supersymmetric reduced Yang-Mills theories

It is shown that there exists an on-shell light cone gauge where half of th e fermionic components of the super vector potential vanish, so that part o f the superspace flatness conditions becomes linear. After reduction to (1 + 1) space-time dimensions, the general solution of this subset of equation s is derived, The remaining non-linear equations are written in a form whic h is analogous to Yang equations, albeit with superderivatives involving si xteen fermionic coordinates. It is shown that this non-linear part may, nev ertheless, be solved by methods similar to powerful techniques previously d eveloped for the (purely bosonic) self-dual Yang Mills equations in four di mensions. (C) 1999 Elsevier Science B.V, All rights reserved.