Lattice geometry of the Hirota equation
Abstract
Description
Geometric interpretation of the Hirota equation is presented as equation describing the Laplace sequence of two-dimensional quadrilateral lattices. Different forms of the equation are given together with their geometric interpretation: (i) the discrete coupled Volterra system for the coefficients of the Laplace equation, (ii) the gauge invariant form of the Hirota equation for projective invariants of the Laplace sequence, (iii) the discrete Toda system for the rotation coefficients, (iv) the original form of the Hirota equation for the tau-function of the quadrilateral lattice.
11 pages, 3 figures, to appear in Proceedings from the Conference "Symmetries and Integrability of Difference Equations III", Sabaudia, 1998
11 pages, 3 figures, to appear in Proceedings from the Conference "Symmetries and Integrability of Difference Equations III", Sabaudia, 1998