论文标题
椭圆形孤子解决方案：$τ$函数，顶点操作员和双线性身份
Elliptic soliton solutions: $τ$ functions, vertex operators and bilinear identities
论文作者
论文摘要
我们为椭圆形溶液建立了双线性框架，该溶液由Lamé型平面波因子组成。 $τ$以Hirota形式的功能是派生的，并且出现了生成此类$τ$函数的顶点操作员。构建了双线性身份，并制定了计算残基和双线性方程的算法。这些对KDV方程式进行了详细研究，并为KP层次结构进行了概述。研究了椭圆函数时期的退化，从而导致了与三角/双曲和合理功能相关的双线性框架。通过使用所谓的椭圆形$ n $ th的根源来考虑通过分散关系减少。 KDV层次结构的$τ$函数，顶点操作员和双线性方程是从KP获得的。我们还制定了两种方法来计算与拉梅型平面波因子相关的双线性衍生物，这表明这种类型的平面波因导致双线性方程的准仪特性。
We establish a bilinear framework for elliptic soliton solutions which are composed by the Lamé-type plane wave factors. $τ$ functions in Hirota's form are derived and vertex operators that generate such $τ$ functions are presented. Bilinear identities are constructed and an algorithm to calculate residues and bilinear equations is formulated. These are investigated in detail for the KdV equation and sketched for the KP hierarchy. Degenerations by the periods of elliptic functions are investigated, giving rise to the bilinear framework associated with trigonometric/hyperbolic and rational functions. Reductions by dispersion relation are considered by employing the so-called elliptic $N$-th roots of the unity. $τ$ functions, vertex operators and bilinear equations of the KdV hierarchy and Boussinesq equation are obtained from those of the KP. We also formulate two ways to calculate bilinear derivatives involved with the Lamé-type plane wave factors, which shows that such type of plane wave factors result in quasi-gauge property of bilinear equations.
