Abstract:

We present an IST for multidimensional vector fields and use it
i) to solve the Cauchy problem for the dispersionless Kadomtsev-Petviashvili (dKP) equation;
ii) to study the longtime behaviour of its solutions;
iii) to obtain the analytic description of the gradient catastrophe of localized 2-dimensional waves evolving according to the dKP equation.

(joint work with S. Manakov)