Darboux-integrable equations with non-Abelian nonlinearities

2000/11/30 by Nikolai V. Ustinov, Marek Czachor
Physics and Astronomy · #nlin.SI #hep-th #quant-ph

paper · pdf

published as in ''Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Computation, Axiomatics'' (eds. Aerts D., Czachor M. and Durt T.), World Scientific, Singapore, 2002, 335-353 · LaTeX, 19 pages

arxiv created 2002/12/06 · arxiv updated 2009/11/30

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 iρ=[H,f(ρ)], with [f(ρ),ρ]=0, (ii) its generalization involving certain functions f(ρ) which are non-Abelian in the sense that [f(ρ),ρ]≠0, and (iii) the Nahm equations.

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