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

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

1999-04-29

arxiv.org/abs/solv-int/9904024v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, LaTeX209

Scientific paper

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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