论文标题
Ode Affine Lie代数的ODE/IM信函：一种数值方法
ODE/IM correspondence for affine Lie algebras: A numerical approach
论文作者
论文摘要
我们以数值方式研究与简单的代数相关的无链仿型谎言代数（包括异常类型）的ode/im对应关系。我们考虑从修改后的仿射TODA场方程的无质量极限获得的线性问题。我们发现，可集成模型中的Q-函数表示为双线性问题解决方案的内部乘积和线性问题的亚辅助解。使用Cheng的算法获得线性问题的解，我们可以有效地确定Q功能的零，该Q-功能的零是提供Bethe Ansatz方程的溶液。我们以数值计算零，这些零被证明与包括异常类型（异常类型）的简单仿射谎言代数的非线性积分方程的结果一致。通过简单的Lie代数的Dynkin图的折叠过程，我们还找到了非微弱仿射谎言代数的线性问题的对应关系。
We study numerically the ODE/IM correspondence for untwisted affine Lie algebras associated with simple Lie algebras including exceptional type. We consider the linear problem obtained from the massless limit of that of the modified affine Toda field equation. We found that the Q-functions in integrable models are expressed as the inner product of the solution of the dual linear problem and the subdominant solution of the linear problem. Using Cheng's algorithm to obtain the solution of the linear problem, we can determine efficiently the zeros of the Q-function, which is known to provide the solutions of the Bethe ansatz equations. We calculate the zeros numerically, which are shown to agree with the results from the Non-Linear Integral Equations for simply-laced affine Lie algebras including the exceptional type. By the folding procedure of the Dynkin diagrams of simply-laced Lie algebras, we also find the correspondence for the linear problem of the non-simply-laced affine Lie algebras.
