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August  2014, 19(6): 1689-1717. doi: 10.3934/dcdsb.2014.19.1689

## Numerical study of blow-up in solutions to generalized Kadomtsev-Petviashvili equations

 1 Institut de Mathématiques de Bourgogne, Université de Bourgogne, 9 avenue Alain Savary, 21078 Dijon Cedex, France

Received  December 2013 Revised  March 2014 Published  June 2014

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 $n\leq2$.
Citation: Christian Klein, Ralf Peter. Numerical study of blow-up in solutions to generalized Kadomtsev-Petviashvili equations. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1689-1717. doi: 10.3934/dcdsb.2014.19.1689
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