共查询到20条相似文献,搜索用时 15 毫秒
1.
A discrete spectral problem is discussed, and a hierarchy of integrable nonlinear lattice equations related tothis spectral problem is devised. The new integrable symplectic map and finite-dimensional integrable systems are givenby nonlinearization method. The binary Bargmann constraint gives rise to a Backlund transformation for the resultingintegrable lattice equations. 相似文献
2.
The method of nonlinearization of spectral problem is developed and applied to the discrete nonlinear Schr6dinger (DNLS) equation which is a reduction of the Ablowitz-Ladik equation with a reality condition. A new integable symplectic map is obtained and its integrable properties such as the Lax representation, r-matrix, and invariants are established. 相似文献
3.
Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations is derived. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses discrete bi-Hamiltonian structure. A new integrable
symplectic map and finite-dimensional integrable systems are given
by nonlinearization method. The binary Bargmann constraint gives
rise to a Bäcklund transformation for the resulting
integrable lattice equations. At last, conservation laws of the
hierarchy are presented. 相似文献
4.
XU Xi-Xiang 《理论物理通讯》2012,57(6):953-960
A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system. 相似文献
5.
A discrete matrix spectral problem and the associated hierarchy of
Lax integrable lattice equations are presented, and it is shown that
the resulting Lax integrable lattice equations are all
Liouville integrable discrete Hamiltonian systems. A new integrable
symplectic map is given by binary Bargmann constraint of the resulting
hierarchy. Finally, an infinite set of conservation laws is given
for the resulting hierarchy. 相似文献
6.
CHEN Lan-Xin SUN Ye-Peng ZHANG Jun-Xian 《理论物理通讯》2008,49(3):540-544
A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method. Finally, according to another new subalgebra of loop algebra A^-2, its integrable couplings are established. 相似文献
7.
ZHU Jun-Yi GENG Xian-Guo 《理论物理通讯》2007,47(4):577-581
By resorting to the nonlinearization approach, a Neumann constraint associated with a discrete 3 × 3 matrix eigenvalue problem is considered. A new symplectic map of the Neumann type is obtained through nonlinearization of the discrete eigenvalue problem and its adjoint one. The generating function of integrals of motion is presented, by which the symplectic reap'is further proved to be completely integrable in the Liouville sense. 相似文献
8.
The method of nonlinearization of spectral problems is developed to the defocusing nonlinear Schrodinger equation. As an application, an integrable decomposition of the defocusing nonlinear Schrodinger equation is presented. 相似文献
9.
The method of nonlinearization of spectral problems is developed to thedefocusing nonlinear Schrödinger equation. As an application, an integrable decomposition of the defocusing nonlinear Schrödinger equation is presented. 相似文献
10.
Measure synchronization in coupled Hamiltonian systems is a novel
synchronization phenomenon. The measure synchronization on symplectic map is
observed numerically, for identical coupled systems with different
parameters. We have found the properties of the characteristic frequency and
the amplitude of phase locking in regular motion when the measure
synchronization of coupled systems is obtained. The relations between the
change of the largest Lyapunov exponent and the course of phase
desynchronization are also discussed in coupled systems, some useful results
are obtained. A new approach is proposed for describing the measure
synchronization of coupled systems numerically, which is
advantage in judging the measure synchronization, especially for the coupled
systems in nonregular region. 相似文献
11.
XU Xi-Xiang YANG Hong-Xiang LU Rong-Wu 《理论物理通讯》2008,50(12):1269-1275
A semi-direct sum of two Lie algebras of four-by-four matrices is presented, and a discrete four-by-four matrix spectral problem is introduced. A hierarchy of discrete integrable coupling systems is derived. The obtained integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discrete Hamiltonian systems. 相似文献
12.
A semi-direct sum of two Lie algebras of four-by-four
matrices is presented, and a discrete four-by-four matrix spectral problem
is introduced. A hierarchy of discrete integrable coupling systems
is derived. The obtained integrable coupling systems are all written in
their Hamiltonian forms by the discrete variational identity. Finally, we
prove that the lattice equations in the obtained integrable coupling systems
are all Liouville integrable discrete Hamiltonian systems. 相似文献
13.
SHEN Shou-Feng 《理论物理通讯》2005,44(12)
In this letter, the Clarkson-Kruskal direct method is extended to similarity reduce some differentialdifference equations. As examples, the differential-difference KZ equation and KP equation are considered. 相似文献
14.
SHEN Shou-Feng 《理论物理通讯》2005,44(6):964-966
In this letter, the Clarkson-Kruskal direct method is extended to similarity reduce some differentialdifference equations. As examples, the differential-difference KZ equation and KP equation are considered. 相似文献
15.
DONG Huan-He SONG Ming WANG Xue-Lei LI Jian-Jun 《理论物理通讯》2008,49(5):1114-1118
A new and efficient way is presented for discrete integrable couplings with the help of two semi-direct sum Lie algebras. As its applications, two discrete integrable couplings associated with the lattice equation are worked out. The approach can be used to study other discrete integrable couplings of the discrete hierarchies of solition equations. 相似文献
16.
smail Aslan 《理论物理通讯》2014,(5):595-599
The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before. 相似文献
17.
Comment on “A Hierarchy of Integrable Nonlinear Lattice Equations and New Integrable Symplectic Map“
Comment on a recent paper on Commun. Theor. Phys. (Beijing, China) 38 (2002) pp. 523-528. 相似文献
18.
In this paper, the classical Lie group approach is extended to find some Lie point symmetries of differentialdifference equations. It reveals that the obtained Lie point symmetries can constitute a Kac-Moody-Virasoro algebra. 相似文献
19.
LIU Shi-Kuo FU Zun-Tao WANG Zhang-Gui LIU Shi-Da 《理论物理通讯》2008,49(5):1155-1158
In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for three nonlinear differential-difference equations are obtained. 相似文献
20.
Based on a kind of Lie algebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using the methods proposed by Ma and Gao. With the help of variational identity, we get the Hamiltonian structure of the hierarchy. 相似文献