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The τ-function of the quadrilateral lattice

Adam Doliwa

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We investigate the τ-function of the quadrilateral lattice using the nonlocal \bar\partial -dressing method, and we show that it can be identified with the Fredholm determinant of the integral equation which naturally appears within that approach.


PACS

02.30.Rz Integral equations

02.30.Ik Integrable systems

02.10.Ud Linear algebra

MSC

45B05 Fredholm integral equations

37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)

06Bxx Lattices (See also 03G10)

15A15 Determinants, permanents, other special matrix functions (See also 19B10, 19B14)

Subjects

Mathematical physics

Dates

Issue 40 (9 October 2009)

Received 31 December 2008

Published 16 September 2009



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