Numerical study of the Petviashvili equation and dispersive shock waves

Tamara Grava, Christian Klein, Giuseppe Pitton

Research output: Contribution to journalArticle (Academic Journal)peer-review

12 Citations (Scopus)
217 Downloads (Pure)


A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev–Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.
Original languageEnglish
Article number20170458
Number of pages20
JournalProceedings of the Royal Society A: Mathematical and Physical Sciences
Issue number2210
Early online date14 Feb 2018
Publication statusPublished - 28 Feb 2018


  • Dispersive Shock waves
  • Kadomtsev Petviashvili equatuon


Dive into the research topics of 'Numerical study of the Petviashvili equation and dispersive shock waves'. Together they form a unique fingerprint.

Cite this