On the solutions of the CP1 model in (2+1) dimensions

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 Painleve transcendents. Some of the reduced equations do not have the Painleve 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''). (C) 1996 American Institute of Physics.