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Hamiltonian System and Infinite Conservation Laws Associated with a New Discrete Spectral Problem
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作者 LUO Lin FAN En-Gui 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第6期1399-1402,共4页
Starting from a new discrete spectral problem, the corresponding hierarchy of nonlinear lattice equations is proposed. It is shown that the lattice soliton hierarchy possesses the bi-Hamiltonian structures and infinit... Starting from a new discrete spectral problem, the corresponding hierarchy of nonlinear lattice equations is proposed. It is shown that the lattice soliton hierarchy possesses the bi-Hamiltonian structures and infinitely many common commuting conserved functions. Further, infinite conservation laws of the hierarchy are presented. 展开更多
关键词 Hamiltonian system infinite conservation laws discrete spectral problem
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Isospectral and Nonisospectral Lattice Hierarchies Associated with a Discrete Spectral Problem and Their Infinitely Many Conservation Laws
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作者 罗琳 范恩贵 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第1期17-20,共4页
In this paper, based on the discrete zero curvature representation, isospectrai and nonisospectrai lattice hierarchies are proposed. By means of solving corresponding discrete spectral equations, we demonstrate the ex... In this paper, based on the discrete zero curvature representation, isospectrai and nonisospectrai lattice hierarchies are proposed. By means of solving corresponding discrete spectral equations, we demonstrate the existence of infinitely many conservation laws for this two hierarchies and obtain the formulae of the corresponding conserved densities and associated fluxes. 展开更多
关键词 lattice hierarchy conservation laws discrete spectral problem
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AN ABLOWITZ-LADIK INTEGRABLE LATTICE HIERARCHY WITH MULTIPLE POTENTIALS
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作者 Wen-Xiu MA 《Acta Mathematica Scientia》 SCIE CSCD 2020年第3期670-678,共9页
Within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type.The existence of infinitely many symmetr... Within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type.The existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace identity.When the involved two potential vectors are scalar,all the resulting integrable lattice equations are reduced to the standard Ablowitz-Ladik hierarchy. 展开更多
关键词 Integrable lattice discrete spectral problem symmetry and conserved functional
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Hamiltonian System of New Nonlinear Lattice Equations
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作者 赵秋兰 于阳 李雪花 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第4期624-630,共7页
A 3-dimensional Lie algebra sμ(3) is obtained with the help of the known Lie algebra. Based on the sμ(3), a new discrete 3 × 3 matrix spectral problem with three potentials is constructed. In virtue of disc... A 3-dimensional Lie algebra sμ(3) is obtained with the help of the known Lie algebra. Based on the sμ(3), a new discrete 3 × 3 matrix spectral problem with three potentials is constructed. In virtue of discrete zero curvature equations, a new matrix Lax representation for the hierarchy of the discrete lattice soliton equations is acquired. It is shown that the hierarchy possesses a Hamiltonian operator and a hereditary recursion operator, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals. 展开更多
关键词 discrete matrix spectral problem discrete zero-curvature representation discrete Hamiltonian structure
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Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations
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作者 Lin Luo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第2期127-130,共4页
In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curv... In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory. 展开更多
关键词 discrete spectral problem lattice hierarchy algebraic structure master symmetry
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Integrable Hierarchy Covering the Lattice Burgers Equation in Fluid Mechanics:N-fold Darboux Transformation and Conservation Laws 被引量:1
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作者 闻小永 高以天 +3 位作者 薛玉山 郭睿 齐凤华 于鑫 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第9期323-330,共8页
Burgers-type equations can describe some phenomena in fluids,plasmas,gas dynamics,traffic,etc.In this paper,an integrable hierarchy covering the lattice Burgers equation is derived from a discrete spectral problem.N-f... Burgers-type equations can describe some phenomena in fluids,plasmas,gas dynamics,traffic,etc.In this paper,an integrable hierarchy covering the lattice Burgers equation is derived from a discrete spectral problem.N-fold Darboux transformation(DT) and conservation laws for the lattice Burgers equation are constructed based on its Lax pair.N-soliton solutions in the form of Vandermonde-like determinant are derived via the resulting DT with symbolic computation,structures of which are shown graphically.Coexistence of the elastic-inelastic interaction among the three solitons is firstly reported for the lattice Burgers equation,even if the similar phenomenon for certern continuous systems is known.Results in this paper might be helpful for understanding some ecological problems describing the evolution of competing species and the propagation of nonlinear waves in fluids. 展开更多
关键词 discrete spectral problem lattice Burgers equation N-fold Darboux transformation conservationlaws symbolic computation
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