Generating Quadrilateral and Circular Lattices in KP Theory

Abstract

The bilinear equations of the $N$-component KP and BKP hierarchies and a corresponding extended Miwa transformation allow us to generate quadrilateral and circular lattices from conjugate and orthogonal nets, respectively. The main geometrical objects are expressed in terms of Baker functions.

20 pages, 1 figure, LaTeX2e with AMSLaTeX, Babel, graphicx and psfrag packages

References in corpus (6)

• Multidimensional Quadrilateral Lattices are Integrable
• Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies
• Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets
• Discrete Levy Transformations and Casorati Determinant Solutions of Quadrilateral Lattices
• Vectorial Ribaucour Transformations for the Lame Equations
• From Ramond Fermions to Lame Equations for Orthogonal Curvilinear Coordinates

Cited by in corpus (4)

• Desargues maps and the Hirota-Miwa equation
• BKP and CKP revisited: The odd KP system
• Darboux transformations for linear operators on two dimensional regular lattices
• Bäcklund transformations as integrable discretization. The geometric approach