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

Abstract

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 a discussion of the observed blow-up scenarios.

24 pages

References in corpus (4)

• Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
• Remarks on the mass constraint for KP type equations
• Numerical study of blow-up in solutions to generalized Korteweg-de Vries equations
• Blow up for the critical gKdV equation I: dynamics near the soliton