论文标题
扭曲的仿射整合层次结构和孤子解决方案
Twisted Affine Integrable Hierarchies and Soliton Solutions
论文作者
论文摘要
讨论了一类可集成层次结构的系统构造，以扭曲的仿射$ a_ {2r}^{（2）} $ lie lie algebra。时间演化方程的零曲率表示根据其代数结构和其真空溶液进行分类。结果表明，一类模型同时接受零和常数（非零）真空解决方案。另一个基本上是由积分的非本地方程组成，可以分为两个子类，一个属于零真空，另一种是恒定的，无零真空溶液。 真空中的二维计势具有至关重要的成分，并显示出具有真空参数$ v_0 $的功能。 Soliton解决方案是由顶点操作员构建的，顶点运算符为非零真空解决方案，对应于以$ v_0 $为特征的变形。
A systematic construction of a class of integrable hierarchy is discussed in terms of the twisted affine $A_{2r}^{(2)}$ Lie algebra. The zero curvature representation of the time evolution equations are shown to be classified according to its algebraic structure and according to its vacuum solutions. It is shown that a class of models admit both zero and constant (non zero) vacuum solutions. Another, consists essentially of integral non-local equations and can be classified into two sub-classes, one admitting zero vacuum and another of constant, non zero vacuum solutions. The two dimensional gauge potentials in the vacuum plays a crucial ingredient and are shown to be expanded in powers of the vacuum parameter $v_0$. Soliton solutions are constructed from vertex operators, which for the non zero vacuum solutions, correspond to deformations characterized by $v_0$.
