On the solutions of the CP1 model in (2+1) dimensions
- 1 March 1996
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 37 (3) , 1501-1520
- https://doi.org/10.1063/1.531446
Abstract
We use the methods of group theory to reduce the equations of motion of the CP1 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 Painlevé transcendents. Some of the reduced equations do not have the Painlevé property. The existence of a Lax pair, making the model integrable, is hence very unlikely, even though it possesses many properties of integrable systems (such as stable ‘‘numerical solitons’’).Keywords
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