We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and the...We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.展开更多
In order to more accurately and effectively consider the propagation process of solitons in electromagnetic pulse waves and make full use of wavelength division multiplexing,we study a class of high-order three-compon...In order to more accurately and effectively consider the propagation process of solitons in electromagnetic pulse waves and make full use of wavelength division multiplexing,we study a class of high-order three-component Hirota equations by the Riemann-Hilbert method.Under zero boundary conditions and given initial conditions q_(j)(x,0),the N-soliton solutions of the equations are obtained by constructing and solving Riemann-Hilbert problems based on matrix spectral problem.Specifically,we discuss the cases of N=1,2,analyze the dynamical properties of 1-soliton and 2-soliton solutions through numerical simulations,and summarize the effect of integrable perturbations and spectral parameters on soliton motion.展开更多
The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokho...The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.展开更多
This paper aims to construct six-component integrable hierarchies from a kind of matrix spectral problems within the zero curvature formulation.Their Hamiltonian formulations are furnished by the trace identity,which ...This paper aims to construct six-component integrable hierarchies from a kind of matrix spectral problems within the zero curvature formulation.Their Hamiltonian formulations are furnished by the trace identity,which guarantee the commuting property of infinitely many symmetries and conserved Hamiltonian functionals.Illustrative examples of the resulting integrable equations of second and third orders are explicitly computed.展开更多
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
通过分析Bai(Bai Z Z.Block preconditioners for elliptic PDE-constrained optimization problems.Computing,2011,91:379-395)给出的离散分布控制问题的块反对角预处理线性系统,提出了该问题的一个等价线性系统,并且运用带有预处理...通过分析Bai(Bai Z Z.Block preconditioners for elliptic PDE-constrained optimization problems.Computing,2011,91:379-395)给出的离散分布控制问题的块反对角预处理线性系统,提出了该问题的一个等价线性系统,并且运用带有预处理子的最小残量方法对该系统进行求解.理论分析和数值实验结果表明,所提出的预处理最小残量方法对于求解该类椭圆型偏微分方程约束最优分布控制问题非常有效,尤其当正则参数适当小的时候.展开更多
文摘We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.
基金Project supported by Shaanxi Scholarship Council of China(Grant No.2021-030)the Youth Scientific Research Project of Shaanxi Province,China(Grant No.202103021223060)。
文摘In order to more accurately and effectively consider the propagation process of solitons in electromagnetic pulse waves and make full use of wavelength division multiplexing,we study a class of high-order three-component Hirota equations by the Riemann-Hilbert method.Under zero boundary conditions and given initial conditions q_(j)(x,0),the N-soliton solutions of the equations are obtained by constructing and solving Riemann-Hilbert problems based on matrix spectral problem.Specifically,we discuss the cases of N=1,2,analyze the dynamical properties of 1-soliton and 2-soliton solutions through numerical simulations,and summarize the effect of integrable perturbations and spectral parameters on soliton motion.
基金supported in part by NSFC(11975145 and 11972291)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17 KJB 110020)。
文摘The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.
基金supported in part by the NSFC(12271488,11975145,11972291)the Ministry of Science and Technology of China(G2021016032L,G2023016011L)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17 KJB 110020)。
文摘This paper aims to construct six-component integrable hierarchies from a kind of matrix spectral problems within the zero curvature formulation.Their Hamiltonian formulations are furnished by the trace identity,which guarantee the commuting property of infinitely many symmetries and conserved Hamiltonian functionals.Illustrative examples of the resulting integrable equations of second and third orders are explicitly computed.
基金Supported by National Natural Science Foundation of China(1127100861072147)+2 种基金The Science and Technology Department of Henan Province(142300410324142300410253152300410230)
基金Supported by the Science and Technology Plan project of the Educational Department of Shandong Province of China under Grant No. J09LA54the research project of "SUST Spring Bud" of Shandong university of science and technology of China under Grant No. 2009AZZ071
文摘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.
基金Project supported by the National Natural Science Foundation of China(11101195)
文摘通过分析Bai(Bai Z Z.Block preconditioners for elliptic PDE-constrained optimization problems.Computing,2011,91:379-395)给出的离散分布控制问题的块反对角预处理线性系统,提出了该问题的一个等价线性系统,并且运用带有预处理子的最小残量方法对该系统进行求解.理论分析和数值实验结果表明,所提出的预处理最小残量方法对于求解该类椭圆型偏微分方程约束最优分布控制问题非常有效,尤其当正则参数适当小的时候.
