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On the solutions of the $CP^{1}$ model in $(2+1)$ dimensions

High Energy Physics - Theory 2009-10-28 v1 chao-dyn Chaotic Dynamics

Abstract

We use the methods of group theory to reduce the equations of motion of the CP1CP^{1} model in (2+1) dimensions to sets of two coupled ordinary differential equations. We decouple and solve many of these equations in terms of elementary functions, elliptic functions and Painlev{\'e} transcendents. Some of the reduced equations do not have the Painlev{\'e} property thus indicating that the model is not integrable, while it still posesses many properties of integrable systems (such as stable ``numerical'' solitons).

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Cite

@article{arxiv.hep-th/9506068,
  title  = {On the solutions of the $CP^{1}$ model in $(2+1)$ dimensions},
  author = {A. M. Grundland and P. Winternitz and W. J. Zakrzewski},
  journal= {arXiv preprint arXiv:hep-th/9506068},
  year   = {2009}
}

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28 pages