NUMERICAL STUDY OF BLOW-UP IN SOLUTIONS TO GENERALIZED KADOMTSEV-PETVIASHVILI EQUATIONS

We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized initial data with a single minimum and single maximum. In the cases with blow-up, we use a dynamic rescaling to identify the type of the singularity. We present the first discussion of the observed blow-up scenarios. We show that the blow-up in solutions to the L-2 critical generalized Kadomtsev-Petviashvili I case is similar to what is known for the L-2 critical generalized Korteweg-de Vries equation. No blow-up is observed for solutions to the generalized Kadomtsev-Petviashvili II equations for n <= 2.