DECOMPOSING A NEW NONLINEAR DIFFERENTIAL-DIFFERENCE SYSTEM UNDER A BARGMANN IMPLICIT SYMMETRY CONSTRAINT

Xinyue Li; Qiulan Zhao

doi:10.11948/jaac20190003

2019 Volume 9 Issue 5

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Xinyue Li, Qiulan Zhao. DECOMPOSING A NEW NONLINEAR DIFFERENTIAL-DIFFERENCE SYSTEM UNDER A BARGMANN IMPLICIT SYMMETRY CONSTRAINT[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1884-1900. doi: 10.11948/jaac20190003

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Xinyue Li, Qiulan Zhao. DECOMPOSING A NEW NONLINEAR DIFFERENTIAL-DIFFERENCE SYSTEM UNDER A BARGMANN IMPLICIT SYMMETRY CONSTRAINT[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1884-1900. doi: 10.11948/jaac20190003

DECOMPOSING A NEW NONLINEAR DIFFERENTIAL-DIFFERENCE SYSTEM UNDER A BARGMANN IMPLICIT SYMMETRY CONSTRAINT

Xinyue Li¹,
Qiulan Zhao^1, ,

1.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, China

Corresponding author: Email address:xyli@sdust.edu.cn(X. Li)
Fund Project: The authors were supported by the Nature Science Foundation of China (No.11701334) and the Science and Technology plan project of the Educational Department of Shandong Province of China (No. J16LI12)

Abstract

Abstract

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.
- Integrable lattice equations /
- symplectic map /
- implicit symmetry constraint /
- finite-dimensional Hamiltonian system
MSC: 35Q51, 37J10, 37K10

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References

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