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The trace identity is extended to the general loop algebra. The
Hamiltonian structures of the integrable systems concerning vector
spectral problems and the multi-component integrable hierarchy can be
worked out by using the extended trace identity. As its
application, we have obtained the Hamiltonian structures of the Yang
hierarchy, the Korteweg-de--Vries (KdV) hierarchy, the
multi-component Ablowitz--Kaup--Newell--Segur (M-AKNS) hierarchy, the
multi-component Ablowitz--Kaup--Newell--Segur Kaup--Newell
(M-AKNS--KN) hierarchy and a new multi-component integrable hierarchy
separately. 相似文献
2.
For M×N spectral matrix, a kind of operation ? which satisfies combination law (a?b)?c=a?(b?c) is introduced. The discrete multi?component zero-curvature equation is deduced by using the new operation ?, and a simple method for constructing discrete multi-component integrable hierarchy is proposed. As its application, the multi-component Toda hierarchy and its two kinds of integrable couplings are worked out. 相似文献
3.
A practicable way to construct discrete integrable couplings is proposed by making use of two types of semi-direct sum Lie algebras. As its application, two kinds of discrete integrable couplings of the Volterra lattice are worked out. 相似文献
4.
A new m×m matrix Kaup-Newell spectral problem is constructed from a normal 2×2 matrix Kaup-Newell spectral problem,a new integrable decomposition of the Kaup-NeweU equation is presented.Through this process,we find the structure of the r-matrix is interesting. 相似文献
5.
A new approach to formulizing a new high-order matrix spectral
problem from a normal 2× 2 matrix modified Korteweg--de Vries
(mKdV) spectral problem is presented. It is found that the
isospectral evolution equation hierarchy of this new higher-order
matrix spectral problem turns out to be the well-known mKdV equation
hierarchy. By using the binary nonlinearization method, a new
integrable decomposition of the mKdV equation is obtained in the
sense of Liouville. The proof of the integrability shows that
r-matrix structure is very interesting. 相似文献
6.
7.
Regarded as the integrable generalization of Camassa-Holm (CH) equation, the CH equation with self-consistent sources (CHESCS) is derived. The Lax representation of the CHESCS is presented. The conservation laws for CHESCS are constructed. The peakon solution, N-soliton, N-cuspon, N-positon, and N-negaton solutions of CHESCS are obtained by using Darboux transformation and the method of variation of constants. 相似文献
8.
The double Wronskian solutions whose entries satisfy matrix equation for a (2+1)-dimensional breaking soliton equation ((2+ 1)DBSE) associated with the ZS-AKNS hierarchy are derived through the Wronskian technique. Rational and periodic solutions for (2+1)DBSE are obtained by taking special eases in general double Wronskian solutions. 相似文献
9.
A new(γA,σB)-matrix KP hierarchy with two time series γA and σB,which consists of γA-flow,σB-flow and mixed γA and σB-evolution equations of eigenfunctions,is proposed.The reduction and constrained flows of(γA,σB)matrix KP hierarchy are studied.The dressing method is generalized to the(γA,σB)-matrix KP hierarchy and some solutions are presented. 相似文献
10.
A new m × m matrix Kaup-Newell spectral problem is constructed from a normal 2 × 2 matrix Kaup-Newell spectral problem, a new integrable decomposition of the Kaup-Newell equation is presented. Through this process, we find the structure of the r-matrix is interesting. 相似文献
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