2019/04/17 by Kui Chen, Cheng Zhang, Chen, Kui +3
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1904.08108
openalex publication_date 2019/04/17 · openalex created_date 2019/04/25 · openalex updated_date 2026/07/28
In this paper squared eigenfunction symmetry of the differential-difference modified Kadomtsev-Petviashvili (DΔmKP) hierarchy and its constraint are considered. Under the constraint, the Lax triplets of the DΔmKP 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 DΔmKP 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 (DΔKP) system. It was thought the Ragnisco-Tu hierarchy does not exist one-field reduction, but here we find an one-field reduction to reduce the hierarchy to the Volterra hierarchy. Besides, the differential-difference Burgers hierarchy are also investigated in Appendix. A multi-dimensionally consistent 3-point discrete Burgers equation is given.