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A new integrable symplectic map by the binary nonlinearization to the super AKNS system

JOURNAL OF GEOMETRY AND PHYSICS 2017年 121卷 123-137页

作者： Li, Xin-Yue Zhao, Qiu-Lan Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Peoples R China Key Lab Robot & Intelligent Technol Shandong Prov Qingdao 266590 Peoples R China

Based on the constructed new Lie super-algebra from OSP(2,2), the super bi-Hamiltonian structure of a new super AKNS hierarchy is obtained by making use of super-trace identity. For the new super AKNS system, an explicit symmetry constraint between the potentials and the eigenfunctions is proposed. Moreover, the super AKNS system is decomposed into two compatible finite-dimensional super integrable systems and the obtained super systems are proved to be finite-dimensional super integrable Hamiltonian systems in the super-symmetry manifold R-4N/4N. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Orthosymplectic Lie superalgebras Super AKNS hierarchy Explicit symmetry constraint binary nonlinearization

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binary nonlinearization of the Nonlinear Schr?dinger Equation Under an Implicit Symmetry Constraint

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 379-388页

作者： Jing YU Jing-song HE Yi CHENG School of Science Hangzhou Dianzi University Department of Mathematics University of Science and Technology of China School of Science Ningbo University

By modifying the procedure of binary nonlinearization for the AKNS spectral problem and its adjoint spectral problem under an implicit symmetry constraint, we obtain a finite dimensional system from the Lax pair of th... 详细信息

关键词： an implicit symmetry constraint binary nonlinearization AKNS system completely integrable Hamiltonian system

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Bargmann Symmetry Constraint and binary nonlinearization of Super NLS-MKdV Hierarchy

Bargmann Symmetry Constraint and Binary Nonlinearization of ...

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2013 Spring International Conference on Advances in Physics(CAP-S)

作者： Sixing Tao Hui Shi School of Mathematics and Information Science Shangqiu Normal University School of Physics and Electronic Information Shangqiu Normal University

An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R 4N|2N with the corresponding dynamical variables x and t n . The integrals of motion required for Liouville integrability are explicitly given.

关键词： Symmetry Constraints binary nonlinearization Super NLS-MKdV Hierarchy Super Finite Dimensional Integrable Hamiltonian Systems

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Two symmetry constraints for a generalized Dirac integrable hierarchy

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2018年第2期458卷 1073-1090页

作者： Xu, Xi-Xiang Sun, Ye-Peng Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Peoples R China Shandong Univ Finance & Econ Sch Math & Quantitat Econ Jinan 250014 Shandong Peoples R China

By a two-by-two matrix spectral problem, a generalized Dirac integrable hierarchy is presented. A Hamiltonian structure of the obtained hierarchy is established by trace identity, and its Liouville integrability is proved. Then, through Bargmann symmetry constraint, spatial part of the Lax pairs and adjoint Lax pairs is nonlinearized as a completely integrable finite-dimensional Hamiltonian system. Next, under an implicit symmetry constraint, both spatial part and temporal parts of the Lax pairs and adjoint Lax pairs are all nonlinearized as completely integrable finite-dimensional Hamiltonian systems. Ultimately, the involutive representation of solution of the generalized Dirac integrable hierarchy is given. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Generalized Dirac integrable hierarchy Hamiltonian structure Bargmann symmetry constraint Implicit symmetry constraint binary nonlinearization Completely integrable finite-dimensional Hamiltonian system

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binary nonlinearization of the super classical-Boussinesq hierarchy

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Chinese Physics B 2011年第7期20卷 13-21页

作者：陶司兴王惠史会 Department of Mathematics Shangqiu Normal University Department of Mathematics Shanghai University Department of Physics and Information Engineering Shangqiu Normal University

The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.

关键词： symmetry constraints binary nonlinearization super classical-Boussinesq hierarchy super finite-dimensional integrable Hamiltonian systems

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The binary nonlinearization of generalized Toda hierarchy by a special choice of parameters

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2011年第8期16卷 3257-3268页

作者： Zhao, Qiu-Lan Li, Yu-Xia Shandong Univ Sci & Technol Coll Sci Qingdao 266510 Peoples R China Shandong Key Lab Robot & Intelligent Technol Qingdao 266510 Peoples R China

A new discrete matrix spectral problem with two arbitrary constants is introduced. The corresponding 2-parameter hierarchy of integrable lattice equations, which can be reduced to the hierarchy of Toda lattice, is obtained by discrete zero curvature representation. Moreover, the Hamiltonian structure and a hereditary operators are deduced by applying the discrete trace identity. Finally, an integrable symplectic map and a family of finite-dimensional integrable systems are given by the binary nonlinearization for the resulting hierarchy by a special choice of parameters. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Discrete Hamiltonian operator Integrable lattice equation binary nonlinearization Discrete finite-dimensional integrable system

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The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2016年第Jul.期36卷 354-365页

作者： Dong, Huanhe Zhang, Yong Zhang, Xiaoen Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Peoples R China

A discrete matrix spectral problem is presented and the hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established. As to the discrete integrable system, nonlinearization of the spatial parts of the Lax pairs and the adjoint Lax pairs generate a new integrable symplectic map. Based on the theory, a new integrable symplectic map and a family of finite-dimension completely integrable systems are given. Especially, two explicit equations are obtained under the Bargmann constraint. Finally, the symmetry of the discrete equation is provided according to the recursion operator and the seed symmetry. Although the solutions of the discrete equations have been gained by many methods, there are few articles that solving the discrete equation via the symmetry. So the solution of the discrete lattice equation is obtained through the symmetry theory. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Discrete isospectrum system Liouville integrability binary nonlinearization Integrable symplectic map Symmetry

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The Bargmann Symmetry Constraint and binary nonlinearization of the Super Dirac Systems

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Chinese Annals of Mathematics,Series B 2010年第3期31卷 361-372页

作者： Jing YU Jingsong HE Wenxiu MA Yi CHENG School of Science Hangzhou Dianzi University Hangzhou 310018 China Department of Mathematics University of Science and Technology of China Hefei 230026 China Department of Mathematics University of Science and Technology of China Hefei 230026 China Department of Mathematics Ningbo University Ningbo 315211 Zhejiang China. Department of Mathematics and Statistics University of South Florida Florida 33620-5700 USA.

An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-diinensional integrable Hamiltonian systems, defined over the super- symmetry manifold R^4N{2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.

关键词： Symmetry constraints binary nonlinearization Super Dirac systems Super finite-dimensional integrable Hamiltonian systems

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A new integrable symplectic map for 4-field Blaszak-Marciniak lattice equations

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2014年第7期19卷 2324-2333页

作者： Li, Xin-Yue Zhao, Qiu-Lan Li, Yu-Xia Shandong Univ Sci & Technol Coll Sci Qingdao 266590 Peoples R China Shandong Key Lab Robot & Intelligent Technol Qingdao 266590 Peoples R China

Based on a new discrete 4 x 4 matrix spectral problem, a hierarchy of integrable 4-field Blaszak-Marciniak lattice equations with four potentials is constructed. Moreover, a new integrable symplectic map and its evolutive system of conserved integrals are obtained by the binary nonlinearization of spatial parts and the time parts of Lax pairs and their adjoint Lax pairs of the hierarchy. (C) 2013 Elsevier B. V. All rights reserved.

关键词： 4-Field Blaszak-Marciniak lattice equation Discrete zero-curvature representation binary nonlinearization Integrable symplectic map

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An Integrable Symplectic Map of a Differential-Difference Hierarchy

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Communications in Theoretical Physics 2012年第3期57卷 333-338页

作者：董焕河衣芳娇苏杰卢国志 College of Information Science and Engineering Shandong University of Science and Technology Shandong Province Mine Disaster Prevention and Control-Ministry of National Key Laboratories(Foster)

By choosing a discrete matrix spectral problem, a hierarchy of integrable differential-difference equations is derived from the discrete zero curvature equation, and the Hamiltonian structures are built. Through a higher-order Bargmann symmetry constraint, the spatial part and the temporal part of the Lax pairs and adjoint Lax pairs, which we obtained are respectively nonlinearized into a new integrable symplectic map and a finite-dimensional integrable Hamiltonian system in Liouville sense.

关键词： differential-difference equation binary nonlinearization integrable symplectic map

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