The field equations for axially symmetric gravitational fields in 4 + K dimensions with K - dimensional toroidal compatification can be reduced to those of a generalized nonlinear sigma model. The dual symmetry of this model is considered first. Then the soliton transformations for these equations are derived using the method of Belinskii and Zakharov consequently generalizing their results to the higher-dimensional case. From the results of the one-soliton transformation, a series of discrete symmetries generalizing the Neugebauer-Kramer transformation in the four-dimensional case are obtained. The basic properties of these new transformations are studied.