SYMMETRIES AND DROMION SOLUTION OF A (2+1)-DIMENSIONAL NONLINEAR SOHR?DINGER EQUATION

The Painlevé property, infinitely many symmetries and exact solutions of a (2+1)-dimensional nonlinear Schr\ddotodinger equation, which are obtained from the constraints of the Kadomtsev-Petviashvili equation, are studied in this paper. The Painlevé property is proved by the Weiss-Kruskal approach, the infinitely many symmetries are obtained by the formal series symmetry method and the dromion-like solution which is localized exponentially in all directions is obtained by a variable separation method.