Dmitry Zezyulin

The paper concerns non-one-dimensional structures described by nonlinear SchrЁodinger equation with additional potential term. A method for numerical construction of structures of such kind is suggested. The method is based on dynamical interpretation of the equation under consideration. Some exact statements are formulated; they allow (in some cases) to perform demonstrative computation and to list all the types of structures mentioned above. Physical applications of the problem are associated with the theory of a Bose—Einstein condensate. In this context the considered equation is called Gross—Pitaevskii equation and the structures under consideration correspond to macroscopic wave function of the condensate.