On Discrete Symmetries of the Multi-Boson KP Hierarchies

Abstract

We show that the multi-boson KP hierarchies possess a class of discrete symmetries linking them to the discrete Toda systems. These discrete symmetries are generated by the similarity transformation of the corresponding Lax operator. This establishes a canonical nature of the discrete transformations. The spectral equation, which defines both the lattice system and the corresponding Lax operator, plays a key role in determining pertinent symmetry structure. We also introduce a concept of the square-root lattice leading to a family of new pseudo-differential operators with covariance under additional Bäcklund transformations.

11 pgs, LaTeX, IFT-P/75/93, UICHEP-TH/93-17

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Cited by in corpus (2)

• Affine Lie Algebraic Origin of Constrained KP Hierarchies
• Extension of the discrete KP hierarchy