Numerical study of the Kadomtsev–Petviashvili equation and dispersive shock waves-Reference-Cited by-同舟云学术

Numerical study of the Kadomtsev–Petviashvili equation and dispersive shock waves

Published:2018-02 Issue:2210 Volume:474 Page:20170458
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Grava T.¹²^ORCID,Klein C.³^ORCID,Pitton G.¹^ORCID

Affiliation:

1. SISSA, Trieste, Italy

2. School of Mathematics, University of Bristol, UK

3. Institut de Mathématiques de Bourgogne, Université de Bourgogne-Franche-Comté, France

Abstract

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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2017.0458

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