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Multi-Component Matrix KP Hierarchies as Symmetry-Enhanced Scalar KP Hierarchies and Their Darboux-B"acklund Solutions

Henrik Aratyn·Emil Nissimov·Svetlana Pacheva
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Abstract

We show that any multi-component matrix KP hierarchy is equivalent to the standard one-component (scalar) KP hierarchy endowed with a special infinite set of abelian additional symmetries, generated by squared eigenfunction potentials. This allows to employ a special version of the familiar Darboux-B"acklund transformation techniques within the ordinary scalar KP hierarchy in the Sato formulation for a systematic derivation of explicit multiple-Wronskian tau-function solutions of all multi-component matrix KP hierarchies.

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Henrik Aratyn, Emil Nissimov, Svetlana Pacheva. 1999-04-29. Multi-Component Matrix KP Hierarchies as Symmetry-Enhanced Scalar KP Hierarchies and Their Darboux-B"acklund Solutions. https://arxiv.org/abs/solv-int/9904024

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