非对易势KP族的无色散极限与2+1维拟对偶手征模型的解
Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions
摘要：
通常的分散性限制的KP层次不工作的情况下，因变量的值在一个非交换（如矩阵）代数。传递到潜在的KP层次，有一个相应的缩放限制在非交换的情况下，这原来是一个“pseudodual手征模型”在2+1维的层次（“pseudodual”的层次扩展沃德的（修改）可积手征模型）。将标度过程应用于从矩阵线性热族的解生成矩阵（势）KP族的精确解的方法，得到了相应的生成矩阵无色散势KP族的精确解的方法，即伪对偶手征模型族.我们利用这个结果构造了2+1维su（m）伪对偶手征模型的精确解，包括各种多块组态。
英文摘要：
The usual dispersionless limit of the KP hierarchy does not work in the case where the dependent variable has values in a noncommutative (e.g. matrix) algebra. Passing over to the potential KP hierarchy, there is a corresponding scaling limit in the noncommutative case, which turns out to be the hierarchy of a `pseudodual chiral model' in 2+1 dimensions (`pseudodual' to a hierarchy extending Ward's (modified) integrable chiral model). Applying the scaling procedure to a method generating exact solutions of a matrix (potential) KP hierarchy from solutions of a matrix linear heat hierarchy, leads to a corresponding method that generates exact solutions of the matrix dispersionless potential KP hierarchy, i.e. the pseudodual chiral model hierarchy. We use this result to construct classes of exact solutions of the su(m) pseudodual chiral model in 2+1 dimensions, including various multiple lump configurations.
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