Non-symmetric discrete Toda systems from quad-graphs

Details Non-symmetric discrete Toda systems from quad-graphs Non-symmetric discrete Toda systems from quad-graphs

2009-08-19

arxiv.org/abs/0908.2822v1

Applicable Analysis, 2010, 89, No. 4, p. 547-569

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pp

Scientific paper

For all non-symmetric discrete relativistic Toda type equations we establish a relation to 3D consistent systems of quad-equations. Unlike the more simple and better understood symmetric case, here the three coordinate planes of $\mathbb Z^3$ carry different equations. Our construction allows for an algorithmic derivation of the zero curvature representations and yields analogous results also for the continuous time case.

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