Darboux-integrable equations with non-Abelian nonlinearities
Abstract
We introduce a new class of nonlinear equations admitting a representation in terms of Darboux-covariant compatibility conditions. Their special cases are, in particular, (i) the "general" von Neumann equation i=[H,f()], with [f(),]=0, (ii) its generalization involving certain functions f() which are non-Abelian in the sense that [f(),]≠0, and (iii) the Nahm equations.
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