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 共查询到20条相似文献,搜索用时 62 毫秒
1.
Fu-bo Zhu  Jie Ji 《Physics letters. A》2008,372(8):1244-1249
Two hierarchies of multi-component Kaup-Newell equations are derived from an arbitrary order matrix spectral problem, including positive non-isospectral Kaup-Newell hierarchy and negative non-isospectral Kaup-Newell hierarchy. Moreover, new integrable couplings of the resulting Kaup-Newell soliton hierarchies are constructed by enlarging the associated matrix spectral problem.  相似文献   

2.
First, a new multi-component modified Kadomtsev-Petviashvill (mKP) spectral problem is constructed by k-constraint imposed on a general pseudo-differential operator. Then, two hierarchies of multi-component mKP equations are derived, including positive non-isospectral mKP hierarchy and negative non-isospectral mKP hierarchy. Moreover, new integrable couplings of the resulting mKP soliton hierarchies are constructed by enlarging the associated matrix spectral problem.  相似文献   

3.
Lingjun Zhou 《Physics letters. A》2008,372(34):5523-5528
In this Letter, the Darboux transformation for the non-isospectral AKNS hierarchy is constructed. We show that the Darboux transformation for the non-isospectral AKNS hierarchy is not an auto-Bäcklund transformation, because the integral constants of the hierarchy will be changed after the transformation. The transform rule of the integral constants will be also derived. By this means, the soliton solutions of the nonlinear equations derived by the non-isospectral AKNS hierarchy can be found.  相似文献   

4.
于发军  李丽 《中国物理 B》2008,17(11):3965-3973
A hierarchy of non-isospectral Ablowitz-Kaup-Newell-Segur (AKNS) equations with self-consistent sources is derived. As a general reduction case, a hierarchy of non-isospectral nonlinear SchrSdinger equations (NLSE) with selfconsistent sources is obtained. Moreover, a new non-isospectral integrable coupling of the AKNS soliton hierarchy with self-consistent sources is constructed by using the Kronecker product.  相似文献   

5.
A set of multi-component matrix Lie algebra is constructed. It follows that a type of new loop algebra AM-1 is presented. An isospectral problem is established. Integrable multi-component hierarchy is obtained by Tu pattern, which possesses tri-Hamiltonian structures. Furthermore, it can be reduced to the well-known AKNS hierarchy and BPT hierarchy. Therefore, the major result of this paper can be regarded as a unified expression integrable model of the AKNS hierarchy and the BPT hierarchy.  相似文献   

6.
A Multi-component Matrix Loop Algebra and Its Application   总被引:3,自引:0,他引:3  
A set of multi-component matrix Lie algebra is constructed. It follows that a type of new loop algebra A^- M-1 is presented. An isospectral problem is established. Integrable multi-component hierarchy is obtained by Tu pattern, which possesses tri-Hamiltonian structures. Furthermore, it can be reduced to the well-known AKNS hierarchy and BPT hierarchy. Therefore, the major result of this paper can be regarded as a unified expression integrable model of the AKNS hierarchy and the BPT hierarchy.  相似文献   

7.
于发军  李丽 《中国物理 B》2009,18(9):3651-3656
It is shown in this paper that the upper triangular strip matrix of Lie algebra can be used to construct a new integrable coupling system of soliton equation hierarchy. A direct application to the Ablowitz--Kaup--Newell-- Segur(AKNS) spectral problem leads to a novel multi-component soliton equation hierarchy of an integrable coupling system with sixteen-potential functions. It is indicated that the study of integrable couplings when using the upper triangular strip matrix of Lie algebra is an efficient and straightforward method.  相似文献   

8.
Engui Fan 《Physics letters. A》2008,372(42):6368-6374
By introducing a discrete spectral problem, we derive a lattice hierarchy which is integrable in Liouville's sense and possesses a multi-Hamiltonian structure. It is show that the discrete spectral problem converges to the well-known AKNS spectral problem under a certain continuous limit. In particular, we construct a sequence of equations in the lattice hierarchy which approximates the AKNS hierarchy as a continuous limit.  相似文献   

9.
In this paper, a generalized Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy in inhomogeneities of media described by variable coefficients is investigated, which includes some important nonlinear evolution equations as special cases, for example, the celebrated Korteweg–de Vries equation modeling waves on shallow water surfaces. To be specific, the known AKNS spectral problem and its time evolution equation are first generalized by embedding a finite number of differentiable and time-dependent functions. Starting from the generalized AKNS spectral problem and its generalized time evolution equation, a generalized AKNS hierarchy with variable coefficients is then derived. Furthermore, based on a systematic analysis on the time dependence of related scattering data of the generalized AKNS spectral problem, exact solutions of the generalized AKNS hierarchy are formulated through the inverse scattering transform method. In the case of reflectionless potentials, the obtained exact solutions are reduced to n-soliton solutions. It is graphically shown that the dynamical evolutions of such soliton solutions are influenced by not only the time-dependent coefficients but also the related scattering data in the process of propagations.  相似文献   

10.
In this paper, we derive the bi-Hamiltonian structure of a multi-component Camassa-Holm system, which associates with the multi-component AKNS hierarchy and multi-component KN hierarchy via the tri-Hamiltonian duality method. Furthermore, the spectral problems of the dual hierarchies may be obtained.  相似文献   

11.
A set of new multi-component matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A-2M. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the multi-component Hamiltonian structures. As its reduction cases, the multi-component C-KdV hierarchy is given. Finally, the multi-component integrable coupling system of C-KdV hierarchy is presented through enlarging matrix spectral problem.  相似文献   

12.
《Physics letters. A》2006,351(3):125-130
A relation between semi-direct sums of Lie algebras and integrable couplings of continuous soliton equations is presented, and correspondingly, a feasible way to construct integrable couplings is furnished. A direct application to the AKNS spectral problem leads to a novel hierarchy of integrable couplings of the AKNS hierarchy of soliton equations. It is also indicated that the study of integrable couplings using semi-direct sums of Lie algebras is an important step towards complete classification of integrable systems.  相似文献   

13.
Fajun Yu 《Physics letters. A》2011,375(13):1504-1509
Some integrable coupling systems of existing papers are linear integrable couplings. In the Letter, beginning with Lax pairs from special non-semisimple matrix Lie algebras, we establish a scheme for constructing real nonlinear integrable couplings of continuous soliton hierarchy. A direct application to the AKNS spectral problem leads to a novel nonlinear integrable couplings, then we consider the Hamiltonian structures of nonlinear integrable couplings of AKNS hierarchy with the component-trace identity.  相似文献   

14.
A set of new matrix Lie algebra and its corresponding loop algebra are constructed. By making use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equation is generated. As its reduction cases, the multi-component Tu hierarchy is given. Finally, the multi-component integrable coupling system of Tu hierarchy is presented through enlarging matrix spectral problem.  相似文献   

15.
By considering (2+1)-dimensional non-isospectral discrete zero curvature equation, the (2+1)-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of the (2+1)- dimensional Toda lattice hierarchy are given. Finally, the (2+1)-dimensional integrable coupling system of the Toda lattice hierarchy is obtained through enlarging spectral problem.  相似文献   

16.
The bilinear form of the (2+1)-dimensional non-isospectral AKNS system is derived. Its N-soliton solutions are obtained by using the Hirota method. As a reduction, a (2+1)-dimensional non-isospectral Schrodinger equation and its N-soliton solutions are constructed.  相似文献   

17.
《Physics letters. A》2006,359(5):458-466
In the Letter we give new symmetries for the isospectral and non-isospectral Ablowitz–Ladik hierarchies by means of the zero curvature representations of evolution equations related to the Ablowitz–Ladik spectral problem. Lie algebras constructed by symmetries are further obtained. We also discuss the relations between the recursion operator and isospectral and non-isospectral flows. Our method can be generalized to other systems to construct symmetries for non-isospectral equations.  相似文献   

18.
The bilinear form of the (2+1)-dimensional non-isospectral AKNS system is derived. Its N-soliton solutions are obtained by using the Hirota method. As a reduction, a (2+1)-dimensional non-isospectral Schrödinger equation and its N-soliton solutions are constructed.  相似文献   

19.
General N-solitons in three recently-proposed nonlocal nonlinear Schrödinger equations are presented. These nonlocal equations include the reverse-space, reverse-time, and reverse-space–time nonlinear Schrödinger equations, which are nonlocal reductions of the Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy. It is shown that general N-solitons in these different equations can be derived from the same Riemann–Hilbert solutions of the AKNS hierarchy, except that symmetry relations on the scattering data are different for these equations. This Riemann–Hilbert framework allows us to identify new types of solitons with novel eigenvalue configurations in the spectral plane. Dynamics of N-solitons in these equations is also explored. In all the three nonlocal equations, their solutions often collapse repeatedly, but can remain bounded or nonsingular for wide ranges of soliton parameters as well. In addition, it is found that multi-solitons can behave very differently from fundamental solitons and may not correspond to a nonlinear superposition of fundamental solitons.  相似文献   

20.
This paper is devoted to the negative flows of the AKNS hierarchy. The main result of this work is the functional representation of the extended AKNS hierarchy, composed of both positive (classical) and negative flows. We derive a finite set of functional equations, constructed by means of the Miwa's shifts, which contains all equations of the hierarchy. Using the obtained functional representation we convert the nonlocal equations of the negative subhierarchy into local systems of higher order, derive the generating function of the conservation laws and the N-dark-soliton solutions for the extended AKNS hierarchy. As an additional result we obtain the functional representation of the Landau–Lifshitz hierarchy.  相似文献   

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