权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Generalization, Discretization and Application of Nonlinear Integrable Systems Associated with Toroidal Lie Algebra Symmetry

环形李代数对称性非线性可积系统的推广、离散化及应用

基本信息

批准号：
15540208
负责人：
OTHA Yasuhiro
金额：
$ 2.05万
依托单位：
Kobe University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

1.The bilinear form of 1st modified hierarchy is obtained for the discrete equations associated with a modification of toroidal Lie algebra sl^<tor>_2. The method is applicable to multi-component case and a discretization of half of bilinear form for the SU(N) self-dual Yang-Mills equation is constructed.2.The instanton solutions for SU(N) self-dual Yang-Mills equation are reconstructed by taking the Green functions for 4-dimensional Laplacian as the components in the persymmetric determinant solution. The positions and amplitudes of instantons correspond to the phase constants and wave numbers of solitons and appear in the parameters of Green functions.3.The integrable discretization of soliton equations associated with the 2-toroidal symmetry is derived by applying the method of the SU(N) self-dual Yang-Mills case. It is also shown that the hierarchy of equations coincides with the one obtained through the non-isospectral deformation technique.4.By introducing infinitely many independent variables in the Hankel determinant expression of general solution for full-infinite 1-dimensional Toda lattice, it is shown that the components are simply obtained by applying the linear differential operators expressed in terms of the Schur polynomial to the seed function. The generating functions of components are given by the ratio of two Τ functions with a shift of discrete variable.

1.对环面李代数sl^ _2的一个变形所对应的离散方程组，得到了第一变形族的双线性形式<tor>。该方法适用于多分量情形，并构造了SU（N）自对偶Yang-Mills方程的半个双线性形式的离散化。2.以四维Laplacian的绿色函数作为过对称行列式解的分量，重构了SU（N）自对偶Yang-Mills方程的瞬子解。瞬子的位置和振幅对应于孤子的相位常数和波数，并出现在绿色函数的参数中。3.利用SU（N）自对偶Yang-Mills情形的方法，导出了2-环面对称孤子方程的可积离散化。通过在全无限一维户田格通解的Hankel行列式表达式中引入无穷多个独立变量，证明了将Schur多项式表示的线性微分算子应用于种子函数，可以简单地得到通解的分量.分量的母函数由两个T函数之比和离散变量的位移给出。