Communications in Mathematical Physics

, Volume 145, Issue 2, pp 329–344 | Cite as

String vertices, overlap equations, τ functions and the Hirota equation

  • B. E. W. Nilsson
  • P. West
Article

Abstract

String vertices,V, are shown to satisfy a new type of overlap equation of the form\(V \exp \{ ip \cdot Q^i (\xi ^i )\} = V \exp \{ ip \cdot Q^i (\xi ^i )\} \left( {\frac{{d\xi ^j }}{{d\xi ^i }}} \right)^{p^2 /2} \) as well as corresponding equations forAn andBn cycles. A special case of such an equation, when integrated, is shown to be the Hirota equation for the K−P hierarchy.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • B. E. W. Nilsson
    • 1
  • P. West
    • 2
  1. 1.Institute of Theoretical PhysicsChalmers University of TechnologyGoteborgSweden
  2. 2.Mathematics DepartmentKing's College LondonLondon

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