ABSTRACT
In this chapter, the authors generalize the perturbation-reduction method to several dimensions by using the ray method. P. Germain extended the perturbation-reduction method to treat the propagation of waves in both nonlinear and dissipative media. The multidimensional dispersive case, limited to shallow water waves, was treated by Prasad and Ravindran. Hunter extended the perturbation-reduction method to treat non-resonant interaction of several dissipative or dispersive waves. However the far field concept, introduced in Section 2.3, can be suitably extended in order to obtain model equations for multi-dimensional waves as well. The modification of the dominant solitonic shape and the shelf appear to be a characteristic of the three-dimensional propagation, and are due to the geometrical effects on the initial soliton.
