Consistency around a cube property of Hirota’s discrete KdV equation and the lattice sine-Gordon equation. (English) Zbl 07856328
Summary: It has been unknown whether Hirota’s discrete Korteweg-de Vries equation and the lattice sine-Gordon equation have the consistency around a cube (CAC) property. In this paper, we show that they have the CAC property. Moreover, we also show that they can be extended to systems on the 3-dimensional integer lattice.
MSC:
| 39A36 | Integrable difference and lattice equations; integrability tests |
| 39A14 | Partial difference equations |
| 37K60 | Lattice dynamics; integrable lattice equations |
Keywords:
discrete integrable systems; partial difference equation; Lax pair; discrete KdV equation; lattice sine-Gordon equationReferences:
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