Lattice geometry of the Hirota equation

Details Lattice geometry of the Hirota equation Lattice geometry of the Hirota equation

1999-07-08

arxiv.org/abs/solv-int/9907013v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, 3 figures, to appear in Proceedings from the Conference "Symmetries and Integrability of Difference Equations III",

Scientific paper

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.

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