New Trends in Quantum and Classical Kinetic Equations and Related PDEs

Numerical study of break-up in Kadomtsev-Petviashvili equations

Christian Klein

Institut de Mathématiques de Bourgogne

The onset of a dispersive shock in solutions to the Kadomtsev-Petviashvili (KP) equations is studied numerically. First we study the shock formation in the dispersionless KP equation by using a map inspired by the characteristic coordinates for the one-dimensional Hopf equation. This allows to numerically identify the shock and to unfold the singularity. A conjecture for the KP solution near this critical point in the small dispersion limit is presented. It is shown that dispersive shocks for KPI solutions can have a second breaking where modulated lump solutions appear.