共查询到20条相似文献,搜索用时 8 毫秒
1.
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. 相似文献
2.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
Robert Conte K.W. Chow 《理论物理通讯》2006,46(6):961-965
The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known resulr of the integrable Ablowitz-Ladik system. 相似文献
9.
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
10.
In this paper, we present an extended Exp-function method to differential-difference equation(s). With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a series of general solutions in forms of Exp-function. 相似文献
11.
An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schrödinger (GNLS) equation, which can be reduced to classical discrete nonlinear Schrödinger (NLS) equation. Furthermore, all of the linear reductions for the discrete GNLS equation are given through the theory of circulant matrices and the discrete NLS equation is obtained by one of the reductions. At the same time, the recursion operator and symmetries of continuous GNLS equation are successfully recovered by its corresponding discrete ones. 相似文献
12.
YU Fa-Jun ZHANG Hong-Qing 《理论物理通讯》2008,50(9):561-564
It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally. 相似文献
13.
It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of
soliton equation hierarchy in this paper. A direct application to
the fractional cubic Volterra lattice spectral problem leads to a
novel integrable coupling system of soliton equation hierarchy. It
is also indicated that the study of discrete integrable couplings
by using the Kronecker product is an efficient and straightforward method. This method can be used generally. 相似文献
14.
Based on semi-direct sums of Lie subalgebra G, a higher-dimensional 6 × 6 matrix Lie algebra sμ(6) is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is derived from a new discrete six-by-six matrix spectral problem. Moreover, the Hamiltonian forms is deduced for lattice equation in the resulting hierarchy by means of the discrete variational identity -- a generalized trace identity. A strong symmetry operator of the resulting hierarchy is given. Finally, we prove that the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian systems. 相似文献
15.
Exact soliton solutions of the dark discrete nonlinear Schrtidinger (DNLS) equation with nonvanishing boundary conditions are found and especially it is shown that the dark DNLS equation can have both dark and bright soliton solutions. Some solitary wave solutions of the DNLS equation with nonvanishing boundary conditions are also derived. 相似文献
16.
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
17.
The dynamical self-trapping of an excitation propagating on one-dimensional of different sizes with nextnearest neighbor (NNN) interaction is studied by means of an explicit fourth order symplectic integrator. Using localized initial conditions, the time-averaged occupation probability of the initial site is investigated which is a function of the degree of nonlinearity and the linear coupling strengths. The self-trapping transition occurs at larger values of the nonlinearity parameter as the NNN coupling strength of the lattice increases for fixed size. Furthermore, given NNN coupling strength, the self-trapping properties for different sizes are considered which are some different from the case with general nearest neighbor (NN) interaction. 相似文献
18.
By means of a noncommutative differential calculus on function space of discrete Abelian groups and that of the regular lattice with equal spacing as well as the discrete symplectic geometry and a kind of classical mechanical systems with separable Hamiltonian of the type H(p, q) = T(p) + V(q) on regular lattice, we introduce the discrete symplectic algorithm, i.e., the phase-space discrete counterpart of the symplectic algorithm including original symplectic schemes and the jet-symplectic schemes in terms of the discrete time jet bundle formalism, on the regular lattice. We show some numerical calculation examples and compare the results of different schemes. 相似文献
19.
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
20.
Xiao-Yong Wen 《理论物理通讯》2016,66(1):29-34
With the aid of symbolic computation Maple, the discrete Ablowitz-Ladik equation is studied via an algebra method, some new rational solutions with four arbitrary parameters are constructed. By analyzing related parameters, the discrete rogue wave solutions with alterable positions and amplitude for the focusing Ablowitz-Ladik equations are derived. Some properties are discussed by graphical analysis, which might be helpful for understanding physical phenomena in optics. 相似文献