# Bidifferential calculus approach to AKNS hierarchies and their solutions

@article{Dimakis2010BidifferentialCA, title={Bidifferential calculus approach to AKNS hierarchies and their solutions}, author={Aristophanes Dimakis and Folkert Mueller-Hoissen}, journal={Symmetry Integrability and Geometry-methods and Applications}, year={2010}, volume={6}, pages={055} }

We express AKNS hierarchies, admitting reductions to matrix NLS and matrix mKdV hierarchies, in terms of a bidifferential graded algebra. Application of a universal result in this framework quickly generates an infinite family of exact solutions, including e.g. the matrix solitons in the focusing NLS case. Exploiting a general Miura transformation, we recover the generalized Heisenberg magnet hierarchy and establish a corresponding solution formula for it. Simply by exchanging the roles of the… Expand

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