共查询到20条相似文献,搜索用时 15 毫秒
1.
一类孤子方程族及其多个Hamilton结构 总被引:2,自引:0,他引:2
本文建立了一个含11个位势的新的等谱问题,得到了一组新的Lax对,由此得到一类新的孤子方程族.该族是Liouville可积的,具有4-Hamilton结构,且循环算子的共轭算子是一个遗传对称算子.另外,为确切说明所得方程族是一个4-Hamilton结构,在附录中证明了所得的4个Hamilton算子的线性组合恒为Hamilton算子. 相似文献
2.
Staring from a new spectral problem, a hierarchy of the generalized Kaup-Newell soliton equations is derived. By employing the trace identity their Hamiltonian structures are also generated. Then, the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations. The Abel-Jacobi coordinates are introduced to straighten the flows, from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions. 相似文献
3.
构造了loop代数A↑~1的一个高阶子代数,设计了一个新的Lax对,利用屠格式获得了含8个位势的孤立子方程族;利用Gauteax导数直接验证了所得3个辛算子的线性组合仍为辛算子.因此该孤立族具有3-Hamilton结构,具有无穷多个对合的公共守恒密度,故Liouville可积.作为约化情形,得到了2个可积系,其中之一是著名的AKNS方程族. 相似文献
4.
《Chaos, solitons, and fractals》2006,27(3):813-821
The LCZ soliton hierarchy is presented, and their generalized Hamiltonian structures are deduced. From the compatibility of soliton equations, it is shown that this soliton hierarchy is closely related to the Burger equation, the mKP equation and a new (2 + 1)-dimensional nonlinear evolution equation (NEE). Resorting to the nonlinearization of Lax pairs (NLP), all the resulting NEEs are reduced into integrable Hamiltonian systems of ordinary differential equations (ODEs). As a concrete application, the solutions for NEEs can be derived via solving the corresponding ODEs. 相似文献
5.
Staring from a new spectral problem, a hierarchy of the soliton equations is derived. It is shown that the associated hierarchies are infinite-dimensional integrable Hamiltonian systems. By the procedure of nonlinearization of the Lax pairs, the integrable decomposition of the whole soliton hierarchy is given. Further, we construct two integrable coupling systems for the hierarchy by the conception of semidirect sums of Lie algebras. 相似文献
6.
A third Hamiltonian operator is presented for a new hierarchy of bi-Hamiltonian soliton equations, thereby showing that this hierarchy is tri-Hamiltonian. Additionally, an inverse hierarchy of common commuting symmetries is also presented. 相似文献
7.
《数学季刊》2015,(4)
In this paper, a new spectral problem is proposed and the corresponding soliton equations hierarchy are also obtained. Under a constraint between the potentials and the eigenfunctions, the eigenvalue problem is nonlinearized so as to be a new finite-dimensional Hamiltonian system. By resotring to the generating function approach, we obtain conserved integrals and the involutivity of the conserved integrals. The finite-dimensional Hamiltonian system is further proved to be completely integrable in the Liouville sense. Finally, we show the decomposition of the soliton equations. 相似文献
8.
When both Hamiltonian operators of a bi-Hamiltonian system are pure differential operators, we show that the generalized Kupershmidt deformation (GKD) developed from the Kupershmidt deformation in [10] offers an useful way to construct new integrable system starting from the bi-Hamiltonian system. We construct some new integrable systems by means of the generalized Kupershmidt deformation in the cases of Harry Dym hierarchy, classical Boussinesq hierarchy and coupled KdV hierarchy. We show that the GKD of Harry Dym equation, GKD of classical Boussinesq equation and GKD of coupled KdV equation are equivalent to the new integrable Rosochatius deformations of these soliton equations with self-consistent sources. We present the Lax pair for these new systems. Therefore the generalized Kupershmidt deformation provides a new way to construct new integrable systems from bi-Hamiltonian systems and also offers a new approach to obtain the Rosochatius deformation of soliton equation with self-consistent sources. 相似文献
9.
Based on fractional isospectral problems and general bilinear forms, the generalized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy. 相似文献
10.
Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy. 相似文献
11.
Yoshihide Watanabe 《Annali di Matematica Pura ed Applicata》1989,154(1):127-146
Summary A certain super Hamiltonian formalism for evolution equations with odd variables is constructed by establishing the notion of super Hamiltonian operator. A useful criterion for the operator of the special class to be super Hamiltonian is presented, by means of which the two differential operators derived by Manin- Radul and the author from the SKP hierarchy are proved to be super Hamiltonian. 相似文献
12.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(6):1664-1675
A hierarchy of integrable couplings of Volterra lattice equations with three potentials is proposed, which is derived from a new discrete six-by-six matrix spectral problem. Moreover, by means of the discrete variational identity on semi-direct sums of Lie algebra, the two Hamiltonian forms are deduced for each lattice equation in the resulting hierarchy. A strong symmetry operator of the resulting hierarchy is given. Finally, we prove that the hierarchy of the resulting Hamiltonian equations are all Liouville integrable discrete Hamiltonian systems. 相似文献
13.
Eigenfunctions of linearized integrable equations expanded around an arbitrary solution are obtained for the Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy and the Korteweg–de Vries (KdV) hierarchy. It is shown that the linearization operators and the integrodifferential operator that generates the hierarchy are commutable. Consequently, eigenfunctions of the linearization operators are precisely squared eigenfunctions of the associated eigenvalue problem. Similar results are obtained for the adjoint linearization operators as well. These results make a simple connection between the direct soliton/multisoliton perturbation theory and the inverse-scattering based perturbation theory for these hierarchy equations. 相似文献
14.
A new subalgebra of loop algebra Ã1 is first constructed. Then a new Lax pair is presented, whose compatibility gives rise to a new Liouville integrable system(called a major result), possessing bi-Hamiltonian structures. It is remarkable that two symplectic operators obtained in this paper are directly constructed in terms of the recurrence relations. As reduction cases of the new integrable system obtained, the famous AKNS hierarchy and the KN hierarchy are obtained, respectively. Second, we prove a conjugate operator of a recurrence operator is a hereditary symmetry. Finally, we construct a high dimension loop algebra
to obtain an integrable coupling system of the major result by making use of Tu scheme. In addition, we find the major result obtained is a unified expressing integrable model of both the AKNS and KN hierarchies, of course, we may also regard the major result as an expanding integrable model of the AKNS and KN hierarchies. Thus, we succeed to find an example of expanding integrable models being Liouville integrable. 相似文献
15.
新的耦合mKdV方程族及其Liouville可积的无限维Hamilton结构 总被引:3,自引:0,他引:3
根据第Ⅱ屠格式,从一个特征值问题出发,本文推得了一族新的耦合mKdV方程,然后用迹恒等式人出了其无限维Hamilton结构。最后证明了该Hamilton方程族是Liouville可积的,并且有无穷多个彼此对合的公共守恒密度。 相似文献
16.
17.
It is known that the Schrödinger flow on a complex Grassmann manifold is equivalent to the matrix non-linear Schrödinger equation and the Ferapontov flow on a principal Adjoint U(n)-orbit is equivalent to the n-wave equation. In this paper, we give a systematic method to construct integrable geometric curve flows on Adjoint U-orbits from flows in the soliton hierarchy associated to a compact Lie group U. There are natural geometric bi-Hamiltonian structures on the space of curves on Adjoint orbits, and they correspond to the order two and three Hamiltonian structures on soliton equations under our construction. We study the Hamiltonian theory of these geometric curve flows and also give several explicit examples. 相似文献
18.
Integrable couplings,bi‐integrable couplings and their Hamiltonian structures of the Giachetti–Johnson soliton hierarchy
下载免费PDF全文
![点击此处可从《Mathematical Methods in the Applied Sciences》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Ya‐Ning Tang Lei Wang Wen‐Xiu Ma 《Mathematical Methods in the Applied Sciences》2015,38(11):2305-2315
On the basis of zero curvature equations from semi‐direct sums of Lie algebras, we construct integrable couplings of the Giachetti–Johnson hierarchy of soliton equations. We also establish Hamiltonian structures of the resulting integrable couplings by the variational identity. Moreover, we obtain bi‐integrable couplings of the Giachetti–Johnson hierarchy and their Hamiltonian structures by applying a class of non‐semisimple matrix loop algebras consisting of triangular block matrices. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach.It is worth to point that the solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations. 相似文献
20.
Wenxiu MA 《数学年刊B辑(英文版)》2012,33(2):207-224
A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy. 相似文献