Existence and Stability

In this part we consider which problems of soliton science discussed in previous chapters can be solved in more than one spatial dimension*). Here the situation differs radically from the one-dimensional case. As a rule, such systems can be obtained by applying the two-dimensional extension to the corresponding one-dimensional ones [1], and therefore are, generally speaking, weakly non-one-dimensional. In particular, the Kadomtsev-Petviashvili (KP) equation is the KdV two-dimensionalization. To date, this model has been sufficiently well explored via IST-type techniques and algebraic geometry [2].