一族可积系及其可积耦合(英文) 被引量：2

An Integrable System and its Integrable Coupling

下载PDF

导出

摘要基于离散等谱问题得到了一族具有双哈密顿结构的Liouville可积系,然后利用半直和的方法得到了其可积耦合系统. A hierarchy of integrable discrete equations is derived based on discrete isospectral problem. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamihonian structure. Then,integrable couplings of the obtained system is given by means of semi-direct sums of Lie algebras.

作者李柱张玉娟

机构地区信阳师范学院数学与信息科学学院信阳职业技术学院经济贸易系

出处《信阳师范学院学报（自然科学版）》 CAS 2009年第4期493-496,共4页 Journal of Xinyang Normal University(Natural Science Edition)

基金 Young Foundation of Xinyang Normal University(20070207)

关键词等谱问题哈密顿结构可积耦合 isospectral problem hamilton structure integrable coupling

分类号 O175.29 [理学—基础数学]

引文网络
相关文献

参考文献8

1Tu G Z. A trace identity and its application to the theory of discrete integrable systems [ J ]. Journal of Physics A: Mathematical and General ( S1751-8113 ), 1990,23:3903-3922.
2Ma W X. A new hierarchy of Liouville integrable generalized Hamiltonian equations and its reduction[ J]. Chinese Journal of Contemporary Mathematics(S1000-8134) , 1992,13 ( 1 ) :79-89.
3Ablowitz L J. Nonlinear differentinl-differenee equation[ J]. Journal of Mathematical Physics( S0022-2488 ), 1975,16:598-603.
4Ohta Y, Hirota R. A discrete KdV equation and its casorati determinant solution[ J]. Journal of the Physical Society of Japan( S0031-9015 ), 1991,60:2095.
5Blaszak M, Marciniak K. R-matrix approach to lattice integrable Hamiltonian systems [ J ]. Journal of Mathematical Physics ( S0022-2488)., 1994, 35:4661-4682.
6王军民,赵安勇.可作为Bcklund变换的微分差分方程[J].信阳师范学院学报（自然科学版）,2006,19(2):139-140. 被引量：2
7Ma W X, Xu X X. A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations [ J ]. Journal of Physics A : Mathematical and General ( S1751-8113 ) ,2004,37 : 1323-1336.
8Li Z. Discrete integrable system and its coupling[ J]. Chinese Physics B(S1674-1056) ,2009,18 (3) :850-856.

二级参考文献4

1ROGERS C,SCHIEF W K.Intrinsic Geometryof the NLS Equation and its Auto-BT[J].Stud Appl Math,1998,26:267-278.
2COUTE R,MUSETTE M.Painleve Analysis and Backlund Transformation in theKuromoto-Sivashinsky Equation[J].J Phys A:Math and Gen,1989,22:169-177.
3HU X B,ZHU Z N.Some New Results on Blaszak-Marciniak Lattice,Backlund Transformationand Nonlinear Superposition Formular[J].J Phys A,1998,39:4766-4772.
4LEVE D.Nonlinear Differential-Difference Equations as Backlund Transformations[J].JPhys A:Math Gen,1981,14:1082-1098.

共引文献1

1王军民.(2+1)-维破切孤子方程的Jacobi椭圆函数周期解[J].河南师范大学学报（自然科学版）,2009,37(5):8-10. 被引量：3

同被引文献20

1董焕河,张宁,杨记明.广义KN方程族及其Hamilton结构[J].大学数学,2005,21(2):69-72. 被引量：1
2Ma W X.Symmetry constraint of MKdV equations by binary nonlinearation[J].Journal of Physics A:Mathematical and General,1995,219:1083-1091.
3Ma w X,Gan L.Coupling integrable couplings[J].Mod Phys Lett B,2009,23(15):1847-1860.
4Hu X B.A powerful approach to generate new integrable systms[J].Joumal of Physics A:Mathematical and General,1994,27:2497-2541.
5Ma W X,Xu X X.A modified Toda spectral problem and its hierarchy of bi-Hamiltonian lattice equations[J].Journal of Physics A:Mathemati-cal and General,2004,37:1323-1336.
6Ma W X,Fuchssteiner B.Integrable theory of the perturbation equations[J].Chaos,Solitom and Fractals,1996,7:1227-1250.
7Hu X B,Tam H.Applications of Hirota's bilinear formalism to a two dimensional lattice by Leznov[J].Phys Lett A,2000,276:65-72.
8Zhang Y F,Honwah.A few new higher-dimensional Lie algebras and two types of coupling integrable couplings of the AKNS hierarchy and the KNhierarchy[J].CNSNS(2010),Doi:10.1016/j.cnsns.2010.03.004.
9Hu X B,Clarkson P A.Rational solutions of an extended Lokta-Voltrra equation[J].J Non Math Phys,2002,9(Suppl):75-86.
10Ma W X.A new hierarchy of liouville integrable generalized hamiltonian equations and its reduction[J].Chinese Journal of Contemporary Mathematics,1992,13(1):79-89.

引证文献2

1魏媛,李刚.一类高维李代数及其应用[J].信阳师范学院学报（自然科学版）,2011,24(1):30-34. 被引量：2
2李柱.一族多分量的刘维尔可积系及其可积耦合[J].泰山学院学报,2012,34(3):22-34.

二级引证文献2

1李柱.一族多分量的刘维尔可积系及其可积耦合[J].泰山学院学报,2012,34(3):22-34.
2李柱.一族离散的刘维尔可积系及其耦合系统[J].信阳师范学院学报（自然科学版）,2018,31(4):525-529.

1齐美美,于宪伟,张旭.一个新的Liouville可积系及其Hamiltion结构[J].渤海大学学报（自然科学版）,2010,31(4):339-341.
2龚新波,杨耕文.一族Liouville可积系及其Hamilton结构[J].甘肃工业大学学报,2003,29(3):123-125.
3徐西祥.一个新的无限维Liouville可积系及其变换[J].高校应用数学学报（A辑）,1997(2):139-146. 被引量：7
4张玉峰,郭福奎.推广的一类Lie代数及其相关的一族可积系统[J].物理学报,2004,53(5):1276-1279. 被引量：2
5王聪华,张玉峰.Loop代数_2的一个新子代数及其有关的一族新的可积系[J].东北师大学报（自然科学版）,2006,38(3):9-12.
6张玉峰,张鸿庆.一族Liouville可积系及其约束流的Lax表示、Darboux变换[J].应用数学和力学,2002,23(1):23-30. 被引量：2
7张玉峰.一族新的可积Hamilton方程[J].数学物理学报（A辑）,2005,25(1):1-4.
8杨洪祥,杨延珍,孙业朋.一族Liouville可积系及其双Hamilton结构[J].泰安师专学报,2002,24(6):12-14.
9张玉峰,张鸿庆.一族Liouville可积系及其双约束流的Hamilton系统[J].工程数学学报,2002,19(4):81-85. 被引量：3
10郭福奎.一族Liouville可积系及其双Hamilton结构[J].山东科技大学学报（自然科学版）,2000,19(2):7-13. 被引量：3

信阳师范学院学报（自然科学版）

2009年第4期

浏览历史

内容加载中请稍等...