Darboux-integrable equations with non-Abelian nonlinearities

Nikolai V. Ustinov; Marek Czachor

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arXiv · nlin/0011013

Darboux-integrable equations with non-Abelian nonlinearities

Nikolai V. Ustinov·Marek Czachor

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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 $i\dotρ=[H,f(ρ)]$, with $[f(ρ),ρ]=0$, (ii) its generalization involving certain functions $f(ρ)$ which are non-Abelian in the sense that $[f(ρ),ρ]\neq0$, and (iii) the Nahm equations.

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Nikolai V. Ustinov, Marek Czachor. 2002-12-06. Darboux-integrable equations with non-Abelian nonlinearities. https://arxiv.org/abs/nlin/0011013

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