We propose a systematic method for generalizing the integrable couplings of soliton eqhations hierarchy with self-consistent sources associated with s/（4）. The JM equations hierarchy with self-consistent sources is ...We propose a systematic method for generalizing the integrable couplings of soliton eqhations hierarchy with self-consistent sources associated with s/（4）. The JM equations hierarchy with self-consistent sources is derived. Furthermore, an integrable couplings of the JM soliton hierarchy with self-consistent sources is presented by using of the loop algebra sl（4）.展开更多
We propose a method to construct the integrable Rosochatius deformations for an integrable couplingsequations hierarchy.As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy withself-c...We propose a method to construct the integrable Rosochatius deformations for an integrable couplingsequations hierarchy.As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy withself-consistent sources and its Lax representation are presented.展开更多
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...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.展开更多
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 ...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.展开更多
The super-classical-Boussinesq hierarchy with self-consistent sources is considered.Then,infinitely many conservation laws for the integrable super-classical-Boussinesq hierarchy are established.
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...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.展开更多
It is shown that the Kronecker product can be applied to constructing new discrete integrable couplingsystem of soliton equation hierarchy in this paper.A direct application to the fractional cubic Volterra lattice sp...It is shown that the Kronecker product can be applied to constructing new discrete integrable couplingsystem of soliton equation hierarchy in this paper.A direct application to the fractional cubic Volterra lattice spectralproblem leads to a novel integrable coupling system of soliton equation hierarchy.It is also indicated that the study ofdiscrete integrable couplings by using the Kronecker product is an efficient and straightforward method.This methodcan be used generally.展开更多
基金Supported by the Research Work of Liaoning Provincial Development of Education under Grant No,2008670
文摘We propose a systematic method for generalizing the integrable couplings of soliton eqhations hierarchy with self-consistent sources associated with s/（4）. The JM equations hierarchy with self-consistent sources is derived. Furthermore, an integrable couplings of the JM soliton hierarchy with self-consistent sources is presented by using of the loop algebra sl（4）.
基金Supported by the Research Work of Liaoning Provincial Development of Education under Grant No.L2010513
文摘We propose a method to construct the integrable Rosochatius deformations for an integrable couplingsequations hierarchy.As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy withself-consistent sources and its Lax representation are presented.
基金Project supported by the Research work of Liaoning Provincial Development of Education, China (Grant No 2008670)
文摘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.
基金supported by the State Key Basic Research Development Program of China under Grant No.2004CB318000
文摘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.
基金Supported by the Scientific Research Foundation of the Education Department of Liaoning Province under Grant No L2010513.
文摘The super-classical-Boussinesq hierarchy with self-consistent sources is considered.Then,infinitely many conservation laws for the integrable super-classical-Boussinesq hierarchy are established.
基金supported by the Research Work of Liaoning Provincial Development of Education,China (Grant No 2008670)
文摘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.
基金the State Key Basic Research and Development Program of China under Grant No.2004CB318000
文摘It is shown that the Kronecker product can be applied to constructing new discrete integrable couplingsystem of soliton equation hierarchy in this paper.A direct application to the fractional cubic Volterra lattice spectralproblem leads to a novel integrable coupling system of soliton equation hierarchy.It is also indicated that the study ofdiscrete integrable couplings by using the Kronecker product is an efficient and straightforward method.This methodcan be used generally.
