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Volume 9, Number 5, 2019, Pages 1884-1900                                                                DOI:10.11948/jaac20190003
Decomposing a new nonlinear differential-difference system under a Bargmann implicit symmetry constraint
Xinyue Li,Qiulan Zhao
Keywords:Integrable lattice equations, symplectic map, implicit symmetry constraint, finite-dimensional Hamiltonian system.
      Firstly, a hierarchy of integrable lattice equations and its bi-Hamilt-onian structures are established by applying the discrete trace identity. Secondly, under an implicit Bargmann symmetry constraint, every lattice equation in the nonlinear differential-difference system is decomposed by an completely integrable symplectic map and a finite-dimensional Hamiltonian system. Finally, the spatial part and the temporal part of the Lax pairs and adjoint Lax pairs are all constrained as finite dimensional Liouville integrable Hamiltonian systems.
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