Lax pair for the Adler (lattice Krichever–Novikov) system

By F. Nijhoff. 2001

252 citations recorded by the source corpus.

Abstract In the paper Int. Math. Res. Notices 1 (1998) 1 a lattice version of the Krichever–Novikov equation was constructed. We present in this Letter its Lax pair and discuss its elliptic form.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b4afa429253746db61afe4add5b0d90e996ec850

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In Applied Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

Burchnall-Chaundy Theory for q-Difference Operators and q-Deformed Heisenberg Algebras (2003, methodology): “It should be mentioned that this kind of arguments was first used to derive Lax representations for 3D consistent discrete equations on quad-graphs with fields on vertices in [3, 4].”
Discrete nonlinear hyperbolic equations. Classification of integrable cases (2007, methodology): “For d = 2, a decisive step was made in [10] and independently in [19]: it was shown that the integrability in the usual sense of soliton theory (as the existence of a zero curvature representation) follows for two-dimensional systems from the three-dimensional consistency.”
Soliton solutions for ABS lattice equations: I. Cauchy matrix approach (2009, background): “In [11, 19] it was explained how to obtain in general Lax representations for quadrilateral lattice equations which satisfy the multidimensional consistency property.”