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

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

1995-06-09

arxiv.org/abs/hep-th/9506068v1

J.Math.Phys. 37 (1996) 1501-1520

Physics

High Energy Physics

High Energy Physics - Theory

28 pages

Scientific paper

10.1063/1.531446

We use the methods of group theory to reduce the equations of motion of the $CP^{1}$ 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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