Lax equations in 10-dimensional supersymmetric classical Yang-Mills theories

Saveliev and the author recently showed that there exists an on-shell light -cone gauge where the nonlinear part of the field equations reduces to a (s uper) version of the Yang equations that can De solved using methods inspir ed by those previously developed for the self-dual Yang-Mills equations in four dimensions. Here, the analogy between these latter theories and the pr esent ones is extended by writing a set of super linear partial differentia l equations that have consistency conditions derivable from the supersymmet ric Yang-Mills equations in 10 dimensions and are analogues of the Belavin- Zakharov Lax pair. In the simplest example of the two-pole ansatz, the same solution-generating techniques work as in the derivation of the multi-inst anton solutions in the late 1970s. The present Lax representation, however, is only a consequence of (instead of being equivalent to) the field equati ons, in contrast to the Belavin-Zakharov Lax pair.