The τ-function of the quadrilateral lattice

DOI10.1088/1751-8113/42/40/404008zbMATH Open1184.35267arXiv0901.0112OpenAlexW3102506675WikidataQ104434194 ScholiaQ104434194MaRDI QIDQ3654301

Adam Doliwa

Publication date: 5 January 2010

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

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

Full work available at URL: https://arxiv.org/abs/0901.0112

zbMATH Keywords

\(\tau\)-functionDarboux equationsquadrilateral lattice\(\bar{\partial}\)-dressing method

Mathematics Subject Classification ID

Soliton equations (35Q51) Discrete version of topics in analysis (39A12) Fredholm integral equations (45B05) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lattice dynamics; integrable lattice equations (37K60)

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