Properties of the NonAutonomous Lattice SineGordon Equation: Consistency around a Broken Cube Property
Abstract
The lattice sineGordon equation is an integrable partial difference equation on Z^{2}, which approaches the sineGordon equation in a continuum limit. In this paper, we show that the nonautonomous lattice sineGordon equation has the consistency around a broken cube property as well as its autonomous version. Moreover, we construct two new Lax pairs of the nonautonomous case by using the consistency property.
 Publication:

SIGMA
 Pub Date:
 April 2022
 DOI:
 10.3842/SIGMA.2022.032
 arXiv:
 arXiv:2201.11264
 Bibcode:
 2022SIGMA..18..032N
 Keywords:

 lattice sineGordon equation; Lax pair; integrable systems; partial difference equations;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics
 EPrint:
 Some text overlap with our paper arXiv:2102.00684 is caused by our use here of basically the same definition of the CABC property, but the results are totally different