On reductions of the discrete Kadomtsev-Petviashvili-type equations. (English) Zbl 1382.39002
Summary: The reduction by restricting the spectral parameters \(k\) and \(k^{\prime}\) on a generic algebraic curve of degree \(\mathcal{N}\) is performed for the discrete AKP, BKP and CKP equations, respectively. A variety of two-dimensional discrete integrable systems possessing a more general solution structure arise from the reduction, and in each case a unified formula for the generic positive integer \(\mathcal{N}\geqslant 2\) is given to express the corresponding reduced integrable lattice equations. The obtained extended two-dimensional lattice models give rise to many important integrable partial difference equations as special degenerations. Some new integrable lattice models such as the discrete Sawada-Kotera, Kaup-Kupershmidt and Hirota-Satsuma equations in extended form are given as examples within the framework.
MSC:
| 39A12 | Discrete version of topics in analysis |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Keywords:
discrete integrable system; direct linearisation; multi-dimensional consistency; reduction; \(\tau\)-function; discrete KP-type equations; discrete Sawada-Kotera equations; discrete Kaup-Kupershmidt equations; discrete Hirota-Satsuma equationsReferences:
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