ON THE SOLUTIONS OF THE CP1 MODEL IN (2-DIMENSIONS(1))

We use the methods of group theory to reduce the equations of motion o f the CP1 model in (2+1) dimensions to sets of two coupled ordinary di fferential equations. We decouple and solve many of these equations in terms of elementary functions, elliptic functions, and Painleve trans cendents. Some of the reduced equations do not have the Painleve prope rty. The existence of a Lax pair, making the model integrable, is henc e very unlikely, even though it possesses many properties of integrabl e systems (such as stable ''numerical solitons''). (C) 1996 American I nstitute of Physics.