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Dispersionless limit of the noncommutative potential KP hierarchy and
solutions of the pseudodual chiral model in 2+1 dimensions | | Aristophanes Dimakis
; Folkert Muller-Hoissen
; | | Date: |
10 Jun 2007 | | Abstract: | 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 the hierarchy
of Ward’s (modified) integrable chiral model). Applying the scaling procedure
to a method to generate exact solutions of a matrix (potential) KP hierarchy
from solutions of a matrix linear heat hierarchy, leads to a corresponding
method which 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. | | Source: | arXiv, arxiv.0706.1373 | | Services: | Forum | Review | PDF | Favorites | |
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