Premium
Squared eigenfunction symmetry of the D Δ mKP hierarchy and its constraint
Author(s) -
Chen Kui,
Zhang Cheng,
Zhang Dajun
Publication year - 2021
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12399
Subject(s) - hierarchy , mathematics , eigenfunction , constraint (computer aided design) , symmetry (geometry) , pure mathematics , mathematical analysis , physics , geometry , quantum mechanics , eigenvalues and eigenvectors , law , political science
In this paper, squared eigenfunction symmetry of the differential‐difference modified Kadomtsev–Petviashvili (D Δ mKP) hierarchy and its constraint are considered. Under the constraint, the Lax triplets of the D Δ mKP hierarchy, together with their adjoint forms, give rise to the positive relativistic Toda (R‐Toda) hierarchy. An invertible transformation is given to connect the positive and negative R‐Toda hierarchies. The positive R‐Toda hierarchy is reduced to the differential‐difference Burgers hierarchy. We also consider another D Δ mKP hierarchy and show that its squared eigenfunction symmetry constraint gives rise to the Volterra hierarchy. In addition, we revisit the Ragnisco–Tu hierarchy which is a squared eigenfunction symmetry constraint of the differential‐difference Kadomtsev–Petviashvili (D Δ KP) system. It was thought the Ragnisco–Tu hierarchy did not exist one‐field reduction, but here we find a one‐field reduction to reduce the hierarchy to the Volterra hierarchy. Besides, the differential‐difference Burgers hierarchy is also investigated in the Appendix. A multidimensionally consistent three‐point discrete Burgers equation is given.