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1.
本文研究了Kaup-Newell族的分数阶非线性双可积耦合.利用分数阶等谱问题和非半单矩阵Lie代数上的非退化、对称双线性形式,得到了Kaup-Newell族的分数阶非线性双可积耦合,并求出了Kaup-Newell族双可积耦合的分数阶Hamilton结构.本文的方法还可以应用于其它孤子族分数阶可积耦合.  相似文献   

2.
魏含玉  夏铁成 《应用数学》2017,30(4):927-935
本文基于新的非半单矩阵Lie代数,介绍了构造孤子族非线性双可积耦合的方法,由相应的变分恒等式给出了孤子族非线性双可积耦合的Hamilton结构.作为应用,给出Kaup-Newell族的非线性双可积耦合及其Hamilton结构.最后利用源生成理论建立新的公式,并导出带自相容源Kaup-Newell族的非线性双可积耦合方程.  相似文献   

3.
基于新的非半单矩阵李代数,介绍了构造孤子族非线性双可积耦合的方法,由相应的变分恒等式给出了孤子族非线性双可积耦合的Hamilton结构.作为应用,给出了Broer-Kaup-Kupershmidt族的非线性双可积耦合及其Hamilton结构.最后指出了文献中的一些错误,利用源生成理论建立了新的公式,并导出了带自相容源Broer-Kaup-Kupershmidt族的非线性双可积耦合方程.  相似文献   

4.
通过介绍一个含四个位势的4×4矩阵谱问题,得到一个新的非线性发展方程族,其中较有意义的一个方程是耦合Kaup-Newell方程.利用迹恒等式,得到了它的双哈密顿结构.在某个约束条件下,通过特征值问题的非线性化方法,得到了Liouville意义下耦合Kaup-Newell方程新的可积分解.  相似文献   

5.
本文中,我们从一个高阶的方阵谱问题出发得到多向量Kaup-Newell方程的一个可积分解.通过迹恒等式的帮助,得到多向量Kaup-Newell方程族的双哈密顿结构,而且可以发现这个多向量Kaup-Newell方程的时间部分和空间部分的约束流是刘维尔意义下的两个可积哈密顿系统.  相似文献   

6.
本文研究Kaup-Newell方程的Darboux变换的非线性化.基于Kaup-Newell方程的Darboux变换经过非线性化得到的映射是约束Kaup-Newell流的Bcklund变换的假设,本文获得了Darboux矩阵中的位势与特征函数之间的约束,由此实现了Kaup-Newell方程的Darboux变换的非线性化,生成了4个具有相同不变量的可积辛映射.  相似文献   

7.
魏含玉  夏铁成 《数学杂志》2015,35(3):539-548
基于可积耦合的基本理论,我们给出了构造孤子族非线性可积耦合的一般方法,并用相应圈代数上的变分恒等式来求可积耦合的哈密顿结构.作为应用,我们给出了Guo族的非线性可积耦合及其哈密顿结构.最后,给出了Guo族非线性可积耦合的守恒律.  相似文献   

8.
基于可积耦合的基本理论,我们给出了构造孤子族非线性可积耦合的一般方法,并用相应圈代数上的变分恒等式来求可积耦合的哈密顿结构.作为应用,我们给出了Guo族的非线性可积耦合及其哈密顿结构.最后,给出了Guo族非线性可积耦合的守恒律.  相似文献   

9.
本文给出耦合Burgers族的换位表示,并通过对耦合Burgers族Lax系统的非线性化得到一个Bargmann系统,证明该系统为Liouville完全可积的,还给出耦合Burgers族解的对合表示.  相似文献   

10.
基于李超代数,构造了超广义Burgers方程族的非线性可积耦合,并且利用超级恒等式得到了它的超Hamilton结构.此外,该文计算出超广义Burgers方程族的非线性可积耦合的Bargmann对称约束.  相似文献   

11.
With the help of a Lie algebra,two kinds of Lie algebras with the forms of blocks are introduced for generating nonlinear integrable and bi-integrable couplings.For illustrating the application of the Lie algebras,an integrable Hamiltonian system is obtained,from which some reduced evolution equations are presented.Finally,Hamiltonian structures of nonlinear integrable and bi-integrable couplings of the integrable Hamiltonian system are furnished by applying the variational identity.The approach presented in the paper can also provide nonlinear integrable and bi-integrable couplings of other integrable system.  相似文献   

12.
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   

13.
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   

14.
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   

15.
It is shown that the Kanp-Newell hierarchy can be derived from the so-called gen- erating equations which are Lax integrable.Positive and negative flows in the hierarchy are derived simultaneously.The generating equations and mutual commutativity of these flows en- able us to construct new Lax integrable equations.  相似文献   

16.
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   

17.
A four-by-four matrix spectral problem is introduced, locality of solution of the related stationary zero curvature equation is proved. An integrable coupling hierarchy of the Mkdv_integrable systems is presented. The Hamiltonian structure of the resulting integrable coupling hierarchy is established by means of the variational identity. It is shown that the resulting integrable couplings are all Liouville integrable Hamiltonian systems. Ultimately, through the nonisospectral zero curvature representation, a nonisospectral integrable hierarchy associated with the resulting integrable couplings is constructed.  相似文献   

18.
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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