Orthogonal and symplectic matrix integrals and coupled KP hierarchy

Abstract

Orthogonal and symplectic matrix integrals are investigated. It is shown that the matrix integrals can be considered as a $\tau$-function of the coupled KP hierarchy, whose solution can be expressed in terms of pfaffians.

4 pages, LaTeX, no figures. to appear in J. Phys. Soc. Jpn. Vol. 68, No. 9 (1999)

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• Dressing method and the coupled KP hierarchy
• N-soliton solutions to the DKP equation and Weyl group actions
• Dispersionless DKP hierarchy and elliptic Lowner equation
• Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems
• Auxiliary Linear Problem, Difference Fay Identities and Dispersionless Limit of Pfaff-Toda Hierarchy
• Elliptic parametrization of Pfaff integrable hierarchies in the zero dispersion limit
• Linear problems and Bäcklund transformations for the Hirota-Ohta system
• Matrix integral solutions to the discrete KP hierarchy and its Pfaffianized version
• Multi-variable reductions of the dispersionless DKP hierarchy
• Loewner equations and reductions of dispersionless hierarchies